UC-NRLF 


$B    55    bMfl 


CONCISE 

BUSINESS 

ARITHMETIC 


MOORE 

and: 

MINER 


GINN  AND  COMPANY 


^. 


GIFT  OF 


Digitized  by  the  Internet  Archive 

in  2007  with  funding  from 

IVIicrosoft  Corporation 


http://www.archive.org/details/concisebusinessaOOmoorrich 


MOORE  AND  MINER  SERIES 


CONCISE  BUSINESS 
ARITHMETIC 


BY 

JOHN  H.  MOORE 

u 
AND 

GEORGE  W.  MINER 


GINN  AND  COMPANY 

BOSTON     -    NEW   YORK     •     CHICAGO     •     LONDON 
ATLANTA     •    DALLAS     •     COLUMBUS     •     SAN   FRANCISCO 


EDUC. 


ENTEUED    AT    STATIONERS      HALL 


COPYRIGHT,  1915,  BY  GEORGE  W.  MINER 


Practical  Business  Arithmetic 
copyright,  1906,  by  john  h.  moore  and  george  w.  miner 

copyright,  1915,  BY  GEORGE  W.  SIINER 


ALL   RIGHTS   RESERVED 


fgftc   gtftengum   jgregg 

GINN  AND  COMPANY-  PRO- 
PRIETORS •  UOSTON  •  U.S.A. 


PREFACE 

The  "  Concise  Business  Arithmetic  "  has  been  prepared  to  meet 
the  needs  of  those  schools  that  have  short  courses  in  business 
arithmetic.  It  emphasizes  fundamental  processes  and  those  sub- 
jects that  are  commonly  used  in  the  business  world.  The  aver- 
age student  needs  all  the  drill  he  can  get  to  acquire  accuracy 
and  facility  in  the  handling  of  numbers. 

This  book  is  made  up  of  twenty  chapters  selected  from  the 
"  Practical  Business  Arithmetic  "  (Revised)  and  retains  the  fea- 
tures of  that  volume  that  have  been  so  highly  commended  by 
teachers,  namely:  the  presentation  of  each  subject  in  a  logical 
order;  the  selection  of  problems  that  appeal  to  the  needs  and 
the  interest  of  the  student  and  of  the  community  as  well ;  the 
omission  of  complex  and  useless  problems  and  the  inclusion  of 
such  material  as  will  meet  the  needs  of  persons  who  have  time 
for  only  a  brief  study  of  business  arithmetic ;  a  plan  of  grad- 
ing and  grouping  problems  which  aids  the  student  in  acquiring 
facility  and  in  advancmg  his  educational  equipment ;  the  inclu- 
sion of  an  amount  of  work  that  will  contribute  to  real  efficiency ; 
the  development  of  subjects  inductively  and  the  omission  of  set 
rules ;  the  unusual  amount  of  work  in  the  different  chapters. 

The  text  includes  the  computation  of  loss  and  gain  on  the 
sellmg  price,  tests  on  a  time  limit,  additional  work  on  graphs, 
statistical  matter  based  on  the  latest  census,  and  an  appendix 
on  the  varied  uses  of  the  adding  machine. 

As  this  work  is  based  on  the  "  Practical  Business  Arithmetic," 
of  which  the  late  John  H.  Moore  was  the  senior  author,  it  seems 
proper  to  retain  his  name  in  the  first  place  on  the  title-page  of 
this  volume,  the  actual  preparation  of  which  has  necessarily  been 
entirely  in  the  hands  of  the  junior  author  of  the  Moore  and 
Miner  textbooks. 

iii 

459906 


iv  CONCISE  BUSINESS  ARITHMETIC 

Grateful  acknowledgment  for  helpful  service  is  due  to 
Dr.  David  Eugene  Smith,  Professor  of  Mathematics,  Teachers 
College,  Columbia  University,  New  York ;  to  Mr.  George  Abbot 
of  Brown  Bros.  &  Co.,  Boston ;  to  Mr.  H.  T.  Smith,  assistant 
cashier  of  the  Shawmut  National  Bank,  Boston,  for  valuable 
assistance  on  the  chapters  on  interest  and  banking ;  to  Mr.  Wm. 
B.  Medlicott,  Lecturer  on  Property  Insurance  at  Harvard  Uni- 
versity, for  his  work  on  the  chapter  on  property  insurance ;  to 
Mr.  Montgomery  Rollins  of  Boston,  author  of  "  Money  and 
Investments";  to  Mr.  Harold  T.  Sibley  of  Chicago  for  sug- 
gestions on  the  chapter  on  stocks  and  bonds ;  to  Mr.  Alexander 
H.  Sproul  of  the  State  Normal  School,  Salem,  Massachusetts, 
and  to  Mr.  C.  D.  McGregor  of  Des  Moines,  Iowa. 

GEORGE  W.  MINER 


CONTENTS 


FUNDAMENTAL   PROCESSES 

CHAPTER  PAGE 

I.   Introduction 1 

11.   Addition 2 

III.  Subtraction 23 

IV.  Multiplication 36 

V.   Division 52 

VI.   Checking  Results 71 

FRACTIONS 

VII.   Decimal  Fractions 75 

VIII.   Factors,  Divisors,  and  Multiples      .......  95 

IX.   Common  Fractions 101 

X.   Aliquot  Parts 138 

XL  Bills  and  Accounts 150 

DENOMINATE    NUMBERS 

XII.   Denominate  Quantities 169 

PERCENTAGE  AND   ITS  APPLICATIONS 

XIII.  Percentage 175 

XIV.  Commercial  Discounts 188 

XV.   Gain  and  Loss .  196 

XVI.   Marking  Goods 204 

XVII.   Property  Insurance 209 

INTEREST   AND   BANKING 

XVIIL   Interest 216 

XIX.   Bank  Discount 230 

XX.   Domestic  Exchange ,    ,     ,  242 

V 


vi  CONCISE  BUSINESS  ARITHMETIC 

DIVIDENDS  AND   INVESTMENTS 

CHAPTER  PAGE 

XXI.   Stocks  and  Bonds 256 

APPENDIX  A 

Adding  Machines .     273 

APPENDIX  B 

Tables  of  Measures 275 

Business  Abbreviations 278 

Business  Symbols 279 

INDEX   . 281 


CONCISE  BUSINESS  ARITHMETIC 

FUNDAMENTAL   PROCESSES 


CHAPTER  I 

INTRODUCTION 

1.  The  student  who  is  prepared  to  study  business  arithmetic 
must  be  familiar  with  the  ordinary  symbols  used  in  the  state- 
ment or  the  solution  of  problems;  he  must  have  the  ability  to 
read  and  to  write  numbers  with  facility;  he  must  know  the 
fundamentals,  and  he  must  be  able  to  perform  ordinary  opera- 
tions in  United  States  money,  and  in  both  common  and  decimal 
fractions. 

2.  In  this  course  in  business  arithmetic  one  learns  many 
simple  methods  for  handling  numbers  and  solving  problems, 
and  the  adaptation  of  arithmetic  to  important  business  operations ; 
he  also  acquires  skill,  rapidity,  and  accuracy,  and  he  learns  how 
to  prove  his  own  work,  thus  developing  self-reliance.  Because 
arithmetic  deals  with  the  problems  of  the  home  as  well  as  the 
business  office,  the  study  of  its  practical  and  everyday  features 
increases  one's  knowledge  of  the  usages,  the  phraseology,  and 
the  literature  of  business  and  commerce. 

3.  Much  attention  is  given,  in  the  text,  to  the  fundamental 
processes,  for  these  are  at  the  foundation  of  all  arithmetic.  One 
must  acquire  a  high  degree  of  accuracy  and  speed  in  the  hand- 
ling of  these  fundamentals  if  he  is  to  achieve  any  marked  degree 
of  success  in  his  subsequent  work. 

The  text  contains  an  unusual  amount  of  material  for  the  studei  t's  work, 
and  portions  of  it  may  be  omitted,  at  the  discretion  of  the  instructor,  if  the 
advancement  of  the  class  warrants  it. 

1 


CHAPTER  II 

ADDITION 
ORAL  EXERCISE 

1.  Find  the  sum  of  1,  2,  3,  7,  5,  9,  4,  8,  and  6. 

2.  Read  each  of  the  numbers  in  problem  1  increased  by  2  ; 
by  5  ;  by  3 ;  by  7  ;  by  8 ;  by  9 ;  by  17 ;  by  23. 

3.  Find  the  sum  of  8,  7,  9,  5,  6,  11,  and  12. 

4.  Read  each  of  the  numbers  in  problem  3  increased  by  12; 
by  15 ;  by  18;  by  24;  by  42;  by  19;  by  16. 

5.  Illustrate  what  is  meant  by  like  numbers. 

4.  Only  like  numbers  can  he  added. 

5.  To  secure  speed  and  accuracy  in  addition  name  results 
only  and  express  these  in  the  fewest  words  possible. 

Thus,  in  adding  2,  4, 7,  8,  3,  2,  and  8  say  6,  13^  21^  4,  6,  34 ;  do  not  say 
S  and  4  are  6  and  7  are  13  and  8  are  21  and  3  are  24  and  2  are  26  and  8  are  34. 

ORAL  EXERCISE 

Name  the  sum  in  each  of  the  following  problems  : 
1.      2.       3.       4.       5.       6.       7.       8.      9.      10.    11.    12.     13.     14.     15. 

322815813551342 


2 

1 

4 

2 

3 

2 

2 

3 

3 

1 

4 

7 

2 

5 

7 

1 

6 

3 

1 

6 

1 

3 

6 

4 

6 

4 

2 

1 

2 

3 

2 

8 

2 

2 

4 

3 

7 

4 

2 

2 

3 

7 

5 

8 

5 

8 

4 

1 

3 

4 

4 

4 

9 

8 

7 

2 

3 

2 

6 

4 

4 

8 

4 

4 

3 

7 

7 

5 

3 

3 

1 

4 

8 

4 

2 

5 

6 

3 

5 

2 

2 

3 

8 

6 

2 

0 

5 

2 

5 

1 

6 

0 

6 

2 

3 

1 

4 

2 

2 

5 

7 

2 

6 

3 

4 

3 

8 

1 

7 

7 

6 

1 

1 

1 

1 

7 

7 

1 

2 

3 

862242243421112 
2235  18322313  862 
415123241244   987 


ADDITION  3 

6.  Addition  is  the  basis  of  all  mathematical  processes.  It 
constitutes  a  large  part  of  all  the  computations  of  business 
life  and  concerns,  to  some  extent,  every  citizen  of  to-day. 
Ability  to  add  rapidly  and  accurately  is  therefore  a  valuable 
accomplishment. 

7.  Rapid  addition  depends  mainly  upon  the  ability  to  group ; 
that  is,  to  instantly  combine  two  or  more  figures  into  a  single 
number.  In  reading  it  is  never  necessary  to  stop  to  name  the 
individual  letters  in  the  words.  All  the  letters  of  a  word  are 
taken  in  at  a  glance  ;  hence  the  whole  word  is  known  at  sight. 
Words  are  then  grouped  in  rapid  succession  and  a  whole  line 
is  practically  read  at  a  glance.  This  is  just  the  principle  upon 
which  rapid  addition  depends.  From  two  to  four  figures 
should  be  read  at  sight  as  a  single  number,  and  the  group  so 
formed  should  be  rapidly  combined  with  other  groups  until  the 
result  of  any  given  column  is  determined.  This  can  be  done 
only  by  intelligent,  persistent  practice. 

8.  The  following  list  contains  all  possible  groups  of  two 
figures  each. 

ORAL   EXERCISE 

Pronounce  at  sight  the  sum  of  each  of  the  following  groups: 
ab        cde        f        gbij        klmno 
1.    112241334314247 
1312      15232673567 


2.    8 

9 

8 

5 

6 

4 

5 

5 

7 

1 

5 

6 

6 

8 

9 

9 

9 

8 

5 

1 

4 

3 

4 

2 

8 

6 

6 

9 

6 

1 

3.    8 

7 

7 

4 

9 

7 

6 

7 

5 

3 

2 

4 

5 

7 

6 

2 

3 

5 

8 

3 

8 

7 

9 

9 

8 

9 

9 

8 

4 

2 

The  above  exercise  may  be  copied  on  the  board  and  each  student  in  turn 
required  to  name  the  results  from  left  to  right,  from  right  to  left,  from  top 
to  bottom,  and  from  bottom  to  top.  The  drill  should  be  continued  until 
the  sums  can  be  named  at  the  rate  of  150  per  minute.  This  is  the  first 
and  most  important  step  in  grouping. 


CONCISE   BUSINESS  ARITHMETIC 


ORAL 

EXERCISE 

Name  the 

swm 

in  each  i 

?/  ^^6 

;  following  problems  : 

1.      2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

13. 

14. 

15. 

6      7 

3 

5 

6 

7 

9 

9 

9 

1 

2 

5 

8 

2 

8 

3      1 

4 

2 

4 

7 

9 

8 

8 

4 

7 

2 

3 

7 

2 

8      7 

7 

5 

8 

2 

5 

9 

4 

5 

8 

3 

5 

4 

1 

7      9 

6 

9 

3 

9 

8 

4 

7 

1 

1 

7 

9 

5 

9 

3      8 

5 

3 

8 

1 

6 

4 

9 

2 

6 

5 

7 

3 

4 

9      4 

7 

7 

2 

9 

8 

5 

1 

3 

5 

7 

6 

5 

5 

5      6 

6 

8 

2 

4 

4 

3 

6 

3 

6 

8 

7 

4 

6 

5      6 

5 

5 

7 

5 

4 

2 

1 

3 

6 

4 

9 

4 

8 

2      3 

2 

1 

1 

2 

3 

1 

1 

2 

5 

3 

8 

1 

9 

4      3 

3 

1 

4 

2 

1 

5 

6 

4 

5 

9 

7 

6 

6 

Name  tlie  results  only  and  make  groups  of  two  figures  each.  Thus,  in 
problem  1,  beginning  at  the  bottom  and  adding  up,  say  6,  16,  28,  43,  52. 

16-45.  Add  the  numbers  iii  the  exercise  on  page  2  by 
groups  of  two  figures  each. 

9.  It  is  practically  as  easy  to  add  54  and  9,  59  and  6,  etc., 
as  it  is  4  and  9,  9  and  6,  etc.  4  and  9  are  always  equal  to  1 
ten  and  3  units, and  9  and  G  to  1  ten  and  5  units.  Hence  in 
adding  54  and  9  think  of  the  tens  as  increased  by  1,  call  the 
units  3,  and  the  result  is  63 ;  in  adding  59  and  6  think  of  the 
tens  as  6,  the  units  as  5,  and  the  result  as  Q^, 


ORAL  EXERCISE 

Pronounce  at  sight  the  sum  of  each  of  the  following  groups  : 
1.27    48    59    77    58    52    59    75    95    84    39    59    84    76    91 
786878869765988 


2.  75 

59 

77 

88 

74 

23 

24 

44 

89 

78 

67 

37 

m 

58   68 

_8 

9 

9 

5 

6 

8 

9 

9 

9 

9 

9 

7 

7 

4     5 

3.  37 

49 

38 

37 

45 

95 

98 

87 

54 

72. 

63 

42 

73 

97  88 

_5 

_8 

7 

6 

9 

8 

7 

7 

9 

9 

8 

9 

^ 

5    ^ 

ADDITION  5 

10.  In  combining  numbers  between  10  and  20  think  of  them 
as  one  ten  and  a  certain  number  of  units  and  not  as  a  certain 
number  of  units  and  1  ten. 

Thus,  in  combining  17  and  18  think  of  28  and  7,  or  35 ;  in  combining  19 
and  15  think  of  29  and  5,  or  34 ;  and  so  on. 

ORAL  EXERCISE 

Pronounce  at  sight  the  sum  of  each  of  the  following  groups  : 
abode        fghi        jklmno 
1.  12    17    12    16    11    12    18    16    17    11    19    13    18    12    17 
15    17    12    13    14    11    18    12    18    19    15    13    12    14    19 


2.13 

11 

15 

19 

14 

19 

17 

15 

13 

19 

16 

14 

18 

18 

12 

18 

16 

16 

14 

15 

16 

16 

13 

11 

18 

14 

14 

11 

15 

19 

3.11 

17 

12 

17 

15 

15 

12 

18 

16 

14 

19 

14 

19 

17 

11 

11 

14 

13 

13 

17 

15 

17 

16 

16 

13 

19 

18 

13 

11 

15 

The  above  exercise  contains  all  combinations  possible  with  the  numbers 
from  11  to  19  inclusive.  Drill  on  the  exercise  should  be  continued  until  re- 
sults can  be  named  at  the  rate  of  120  per  minute. 

11.  Numbers  between  10  and  20  may  be  combined  with  num- 
bers above  20  in  practically  the  same  manner  as  in  §  10 

Thus,  in  adding  62  and  12  think  of  72  and  2,  or  74 ;  in  adding  79  and  17 
think  of  89  and  7,  or  96. 

ORAL  EXERCISE 

Pronounce  at  sight  the  sum  of  each  of  the  following  groups: 
1.  25    48    59    87    91    75    86    75    48    78    57    89    37    m    75 
17    17    16    14    18    18    19    12    16    13    16    14    17    18    14 


I 


2.29 

47 

83 

92 

36 

54 

59 

78 

67 

92 

77 

86 

53 

78 

85 

13 

14 

19 

14 

19 

13 

18 

15 

13 

13 

19 

19 

17 

14 

14 

3.31 

32 

45 

69 

74 

95 

98 

92 

96 

87 

86 

34 

43 

64 

38 

19 

17 

19 

15 

8 

18 

14 

19 

15 

17 

19 

18 

18 

19 

17 

64, 

71,  8,  85. 

14. 

8's  from  10  to  138. 

15. 

7's  from  19  to  152. 

16. 

6's  from  20  to  128. 

17. 

6's  from  15  to  111. 

18. 

9's  from  12  to  102. 

19. 

8's  from  17  to  113. 

20. 

7's  from  24  to  108. 

21. 

6's  from  27  to  117. 

22. 

4's  from  19  to  183. 

23. 

ll's  from  14  to  102. 

24. 

12's  from  17  to  161. 

25. 

13's  from  17  to  121. 

6  CONCISE   BUSINESS   ARITHMETIC 

ORAL  EXERCISE 

1.  Count  by  7's  from  1  to  85. 
Solution.     8,  15,  22,  9,  36,  43,  50,  7, 

Count  hy : 

2.  2's  from  39  to  b^, 

3.  5's  from  11  to  86. 

4.  6's  from  15  to  63. 

5.  5's  from  2  to  107. 

6.  7's  from  11  to  60. 

7.  8's  from  25  to  89. 

8.  9's  from  31  to  112. 

9.  8's  from  32  to  192. 

10.  7's  from  18  to  102. 

11.  6's  from  72  to  126. 

12.  9's  from  10  to  136. 

13.  9's  from  17  to  152. 
26.  Beginning  at  1  count  by  4's  to  17 ;  going  on  from  17 

count  by  7's  to  52  ;  from  52  count  by  9's  to  133  ;  from  133 
count  by  5's  to  158  ;  from  158  count  by  12's  to  206  ;  from 
206  count  by  13's  to  271. 

This  exercise  furnishes  one  of  the  best  possible  drills  in  addition,  and  it 
should  be  continued  until  the  successive  results  can  be  named  at  the  rate  of 
150  per  minute. 

12.  If  the  student  is  accurate  and  rapid  in  making  groups 
of  two  figures  each,  he  is  ready  for  practice  in  groups  of  three 
figures  each.  In  the  following  exercise  are  all  the  possible 
groups  of  three  figures  each. 

ORAL  EXERCISE 

Name  at  sight  the  sum  of  each  of  the  following  groups: 

4,  2,  and  3  should  be  thought  of  as  9  just  as  p-e-n  is  thought  of  as  pen. 

1.  419811318145178 
131223173314414 
332175631941641 


ADDITION  7 

2.  161412111176981 
412122911666555 
925231187811117 


3. 

6 

5 

2 

5 

2 

3 

9 

2 

2 

2 

2 

6 

1 

1 

2 

1 

1 

3 

3 

3 

2 

2 

8 

7 

6 

5 

1 

1 

1 

2 

5 

5 

6 

2 

4 

3 

2 

2 

2 

2 

2 

1 

5 

4 

4 

4. 

3 

2 

1 

2 

2 

6 

2 

6 

5 

5 

7 

1 

1 

1 

1 

2 

2 

1 

7 

6 

8 

6 

2 

2 

2 

2 

1 

1 

6 

9 

2 

2 

3 

7 

9 

2 

7 

6 

9 

8 

5 

2 

1 

9 

9 

5. 

9 

8 

9 

8 

7 

3 

4 

5 

6 

6 

5 

4 

3 

3 

4 

1 

1 

1 

1 

1 

5 

8 

7 

7 

7 

5 

4 

4 

4 

4 

8 

8 

7 

7 

7 

5 

4 

5 

9 

8 

6 

7 

9 

8 

6 

6. 

5 

6 

6 

9 

5 

7 

3 

4 

9 

6 

6 

8 

3 

3 

3 

5 

7 

6 

4 

4 

3 

4 

4 

4 

8 

7 

4 

9 

4 

4 

5 

7 

9 

9 

4 

4 

6 

4 

8 

6 

6 

8 

9 

5 

4 

7. 

3 

4 

6 

9 

8 

5 

4 

3 

3 

2 

3 

3 

4 

5 

8 

8 

7 

6 

9 

9 

9 

7 

8 

3 

5 

3 

7 

7 

8 

8 

9 

9 

6 

9 

9 

9 

8 

8 

9 

6 

8 

9 

7 

9 

8 

8. 

8 

5 

4 

3 

3 

5 

2 

3 

3 

4 

5 

7 

7 

5 

4 

8 

8 

9 

8 

7 

2 

4 

3 

7 

6 

7 

9 

8 

7 

6 

9 

5 

6 

7 

3 

5 

9 

6 

7 

8 

9 

9 

9 

8 

7 

9. 

3 

3 

2 

2 

3 

3 

4 

5 

7 

9 

9 

9 

7 

3 

6 

6 

3 

4 

4 

3 

6 

6 

7 

8 

7 

6 

5 

6 

3 

4 

9 

5 

8 

7 

4 

8 

6 

7 

8 

7 

5 

4 

3 

3 

2 

10. 

2 

2 

3 

4 

5 

7 

2 

2 

3 

4 

5 

7 

9 

6 

6 

4 

9 

6 

5 

6 

7 

4 

8 

5 

5 

6 

7 

9 

6 

5 

5 

9 

6 

8 

8 

8 

4 

9 

9 

7 

7 

7 

6 

5 

4 

11. 

8 

8 

9 

2 

2 

3 

4 

5 

6 

8 

8 

9 

6 

8 

7 

5 

8 

3 

3 

7 

5 

5 

5 

8 

8 

5 

4 

5 

7 

3 

3 

2 

2 

8 

9 

7 

5 

9 

9 

6 

5 

4 

3 

2 

2 

This  exercise  should  be  drilled  upon  until  the  sums  of  the  groups,  in  any. 
order,  can  be  named  at  the  rate  of  120  per  minute. 


8  CONCISE   BUSINESS   ARITHMETIC 


( 

ORAL 

EXERCISE 

1-15.    Turn  to  the 

exercise 

!  on  page  2  and  find  the 

sum  of 

the 

numbers 

given. 

Name  results  on 

ly,  and  make  \ 

groups  of  three  figures  each. 

Thus,  in 

problem  1,  say 

9,  23,  37, 

^^. 

Add  from  the  bottom  up  and  check  the  work  by  adding  from  the  top  down. 

Find  the  Bum  in  each  of  the 

following  problems: 

16. 

17.     18. 

19. 

20. 

21. 

22. 

23.    24.    25. 

26. 

27. 

28. 

29. 

30. 

1 

3      1 

4 

2 

2 

2 

4      4      5 

1 

2 

9 

5 

4 

1 

1      3 

3 

3 

1 

6 

3      9      5 

7 

4 

0 

7 

3 

1 

1      4 

1 

5 

2 

2 

4      5      0 

2 

4 

1 

2 

1 

2 

1      3 

1 

3 

1 

4 

18      8 

9 

2 

8 

0 

1 

2 

4      1 

4 

6 

4 

5 

8      3      2 

0 

3 

0 

0 

6 

2 

2      3 

8 

1 

1 

2 

17      1 

1 

5 

2 

5 

8 

2 

4      2 

2 

2 

2 

2 

3      8      3 

5 

7 

2 

6 

1 

5 

2      1 

4 

5 

3 

7 

6      2      7 

3 

7 

2 

6 

6 

1 

2      9 

4 

3 

2 

3 

18      2 

2 

1 

6 

0 

7 

5 

1      8 

3 

4 

2 

1 

2      9      9 

6 

7 

2 

3 

3 

3 

5      2 

3 

3 

6 

9  . 

3      3      1 

2 

8 

2 

6 

3 

1 

3      1 

3 

3 

1 

0 

5      6      3 

7. 

0 

4 

1 

1 

3 

2      7 

2 

4 

3 

0 

2      8      8 

.4 

7 

2 

5 

9 

5 

4      2 

5 

2 

4 

8 

5      12 

3 

3 

2 

3 

2 

2 

4      1 

4 

4 

3 

2 

2      0      4 

3 

0 

5 

2 

1 

1 

2      1 

2 

6 

6 

4 

4      6      6 

3 

6 

2 

5 

8 

8 

6      2 

3 

3 

3 

5 

2      4      4 

3 

3 

2 

8 

2 

1 

2      6 

5 

1 

1 

1 

3      0      5 

6 

1 

6 

2 

1 

4 

4      1 

3 

7 

2 

9 

3      7      9 

1 

5 

7 

5 

7 

3 

5      2 

2 

2 

6 

2 

2      3      1 

7 

3 

3 

7 

2 

4 

2      5 

6 

1 

3 

1 

3      0      3 

2 

2 

1 

3 

1 

4 

2      1 

2 

1 

2 

2 

7      7      7 

1 

1 

9 

2 

2 

9 

7      2 

2 

3 

8 

3 

12      3 

9 

1 

2 

5 

2 

1 

3      4 

4 

4 

1 

7 

7      10 

0 

8 

4 

8 

4 

2 

1      3 

7 

3 

2 

5 

7      6      5 

5 

2 

4 

4 

3 

1 

6      2 

1 

5 

5 

3 

2      3      2 

8 

1 

3 

6 

3 

2 

3      1 

1 

2 

1 

1 

2      12 

1 

5 

7 

1 

1 

ADDITION 


9 


13.  It  is  always  an  advantage  to  find  groups  of  figures  aggre- 
gating 10  and  20  in  the  body  of  a  column. 

These  groups  should  be  added  immediately  to  the  sum  already  obtained 
by  simply  combining  the  tens  of  the  two  numbers.  It  is  not  a  good  plan, 
however,  to  take  the  digits  in  irregular  order  in  order  to  form  groups  of 
10  and  20. 

ORAL  EXERCISE 

Find  the  sum  in  each  of  the  following  problems^  taking  advan- 
tage of  groups  of  10  and  20  wherever  possible : 


1.      2.       3.      4. 

6 
4 


1  21  71 
9j  8J  3j 
71  41  5' 
3J  6j  5. 

2  7  7 


J     9      2 


5.      6.      7.      8.      9.     10.  11.     12.  13.    14.    15. 

525343  78  259 

554325  5   4  789 

56785  56  321 

79874  02  581 

431236  9   7  525 


16.  17.  18.  19.  20.  21.  22.  23.  24.  25.  26.  27.  28.  29.  30. 


3J  8 

71 

2 

1 

6 


91  1 


6   5 


2   4   4 


6 


2-2   422393 


31.  32.  33.  34.  35.  36.  37.  38.  39.  40.  41.  42.  43.  44.  45. 


2 

31 

91 

2 

8 

4 

9 

■     9j 

7j 

9J 

7 

9 

Q  6  6 

7  7  5 

7  8  6 

9  7 


8   7 


6  2  7  6 

9  8  9  7 

5  9  9  4 

6  9  2  9 


46.  47.  48.  49.  50.   51.  52.  53.  54.  55.  56.  57.  58.  59.  60. 

38    42     25     35     46     14     21     12    18    29    57  17    13    14    15 

0  32554627 
634768672 
6  84898858 
8       67455      236 


10  CONCISE   BUSINESS   ARITHMETIC 

14.  When  three  figures  are  in  consecutive  order  the  sum  may 
be  found  by  multiplying  the  middle  figure  by  3 ;  when  five 
figures  are  in  consecutive  order  the  sum  may  be  found  by  mul- 
tiplying the  middle  figure  by  5 ;  etc. ;  or  the  sum  of  any  num- 
ber of  consecutive  numbers  may  be  found  by  taking  one  half  the 
sum  of  the  first  and  last  numbers  and  multiplying  it  by  the 
number  of  terms. 

ORAL  EXERCISE 

By  inspection  find  the  sum  of: 
1.     2.      3.      4.      5.      6.      7.      8.      9.     10.     11.     12.     13.    14.     15. 

7  10    13    16    19    22    25    28    31    34     37     40     43     46     49 

8  11    14    17    20    23    26    29    32    35     38    41    44    47     50 
91215182124273033363942454851 

16.    17.    18.    19.    20.     21.    22.    23.    24.    25.     26.      27.     28.    29.     30. 

10  15  20  25  30  35  40  45  50  55  60  Q^     70  75  80 

11  16  21  26  31  36  41  46  51  ^  61  m    71  76  81 

12  17  22  27  32  37  42  41  52  57  62  67  72  77  82 

13  18  23  28  33  38  43  48  53  58  63  68  73  78  83 
14192429343944495459  64697479  84 

31.  32.  33.  34.  35.  36.  37.  38.  39.  40.  41.  42.  43.  44.  45. 

7  10  13  16  19  22  25  28  31  34  37  40  43  46  49 

8  11  14  17  20  23  26  29  32  35  38  41  44  47  50 

9  12  15  18  21  24  27  30  33  36  39  42  45  48  51 

10  13  16  19  22  25  28  31  34  37  40  43  46  49  52 

11  14  17  20  23  26  29  32  35  38  41  44  47  50  53 

12  15  18  21  24  27  30  33  36  39  42  45  48  51  54 

13  16  19  22  25  28  31  34  37  40  43  46  49  52  3^ 

14  17  20  23  26  29  32  35  38  41  44  47  50  53  m 

15  18  21  24  27  30  33  36  39  42  45  48  51  54  57 

16  19  22  25  28  31  34  37  40  43  46  49  52  55  58 
1720232629323538414447505356  59 

15.  When  a  figure  is  repeated  several  times  the  sum  may  be 
found  by  multiplication. 


ADDITION  11 

ORAL  EXERCISE 

^y  inspection  find  the  sum  of : 

1.      2.       3.      4.       5.       6.       7.       8.        9.      10.  11.     12.  13.  14.     15. 

434537       8       8     15       6  T       8  15  13      9 

97453757     15      687  14  13      8 

984597      5      9    15    12  7      8  15  13      8 

989598      6      98    12  77  14  79 

989988698     12  78  15  78 


16. 

17. 

18. 

19. 

20. 

21. 

22. 

23. 

24. 

25. 

26. 

27. 

28. 

29. 

30. 

3 

7 

4 

2 

7 

5 

12 

2 

4 

6 

8 

9 

8 

5 

16 

3 

7 

4 

2 

7 

5 

5 

2 

4 

6 

8 

9 

8 

5 

16 

3 

7 

4 

2 

4 

5 

5 

2 

4 

6 

8 

9 

8 

5 

16 

2 

2 

7 

8 

4 

4 

5 

3 

5 

4 

3 

5 

8 

5 

16 

2 

2 

7 

8 

2 

4 

5 

3 

5 

4 

3 

5 

8 

5 

20 

2 

2 

7 

8 

2 

4 

5 

3 

5 

4 

3 

5 

9 

8 

1 

16.  In  all  written  work  make  plain,  legible  figures  of  a 
uniform  size,  write  them'  equal  distances  from  each  other, 
and  be  sure  that  the  units  of  the  same  order  stand  in  the 
same   vertical  column. 

/     Z     ^     4^ur     ^    y    <^    f    ^ 

17.  Many  of  the  errors  that  occur  in  business  are  in  simple 
addition.  Errors  in  addition  result  from  two  main  causes: 
irregularity  in  the  placing  of  figures ;  poor  figures. 

18.  In  business  it  is  important  that  figures  be  made  rapidly; 
but  rapidity  should  never  be  secured  at  the  expense  of  legibility. 

WRITTEN  EXERCISE 


Copy  and 

find  the 

sum  of: 

1. 

2. 

3. 

4. 

5. 

6. 

1745 

1842 

1249 

4271 

6229 

1481 

1862 

1695 

1810 

8614 

4813 

1862 

7529 

4716 

6241 

9217 

7142 

4129 

8721 

8412 

1728 

8214 

6212 

2412 

CB 


12 


CONCISE   BUSINESS   ARITHMETIC 


7. 

8. 

9. 

10. 

11. 

12. 

4216 

2110 

4142 

1061 

4113 

4112 

8912 

8420 

4347 

1875 

8217 

1012 

4729 

•  1641 

1012 

6214  ' 

8614 

1862 

8624 

1722 

1816 

1931 

1692 

1721 

4829 

1837 

4112 

1648 

1591 

1692 

6212 

4216 

4210 

1721 

1686 

1486 

4110 

4117 

1618 

1728 

2172 

4112 

4210 

1832 

4060 

1421 

1754 

1010 

19.  The  simplest  way  to  check  addition  is  to  add  the  columns 
in  reverse  order.  If  the  results  obtained  by  both  processes 
agree,  the  work  may  be  assumed  to  be  correct. 

20.  In  adding  long  columns  of  figures  it  is  generally  advis- 
able to  record  the  entire  sum  of  each  column  separately  ;  then 
if  interruptions  occur,  it  will  not  be  necessary  to  re-add  any  por- 
tions already  completed.  After  the  total  of  each  column  has 
been  found  the  entire  total  may  be  determined  by  combining 
the  separate  totals  of  the  columns.    • 

21.  The  best  way  to  test  the  accuracy  of  columns  added  in  this 
manner  is  to  begin  at  the  left  and  repeat  the  addition  in  reverse 
order.  The  entire  total  of  each  column  should  again  be  written 
and  the  complete  total  of  the  problem  found  by  adding  the  sepa- 
rate totals  of  the  several  columns.  If  the  results  obtained  by 
the  two  processes  agree,  the  work  may  be  assumed  to  be  correct. 

22.  Example.  Find  the  sum  of  54,669,  15,218,  36,425, 
45,325,  and  68,619.      Check  the  result. 

Solution.  Beginning  at  the  bottom  of  the 
right-hand  column,  add  each  column  in  regu- 
lar order  and  write  the  entire  totals  as  shown 
in  (a).  Beginning  at  the  top  of  the  left- 
hand  column  again  add  each  column  and 
write  the  entire  totals  as  shown  in  (h).  Next 
add  the  totals  obtained  by  the  first  and 
second  additions  and  compare  the  results. 
Since  the  total  shown  by  (a)  is  equal  to  the 
total  shown  by  (6),  the  result,  220,256,  is  assumed  to  be  correct, 
addition  should  be  carefully  checked. 


(J) 

54669 

(a) 

19 

15218 

36 

28 

36425 

12 

21 

45325 

21 

12 

68619 

28 

36 

220256 

19 

220256 

220256 

med  to  be  correct.  All  work  in 

ADDITION  13 

WRITTEN  EXERCISE 

See  how  many  times  the  following  numbers  can  he  written  in 
one  minute.      Write  each  number  in  form  for  vertical  addition. 

1.  426579.  3.  ^7983.21.  5.  170812.34. 

2.  123987.  4.  $4080.91.  6.  $41182.50. 

Thus,  in  repeating  the  number  in  problem  1  write  it  as  follows: 


^  z    ^  ^  7 

^ 

A^  z    C   ^  7 

f 

A^  Z     ^    S-  7 

^ 

^^   Z     /   JT  7 

f 

<ii^. 

Be  sure  that  the  spacing  between  the  lines  and  between  the  columns  is 
uniform.  Increase  the  speed  gradually  until  from  150  to  200  figures  can 
be  written  per  minute. 

23.  Skill  in  writing  figures  from  dictation  should  be  culti- 
vated. The  dictation  should  be  slow  at  first,  but  it  should  be 
gradually  increased  until  the  requisite  speed  is  acquired. 

24.  In  calling  off  numbers  to  another  great  care  should  be 
taken  in  order  that  no  errors  may  be  made.  In  reading 
United  States  money  the  word  dollars  should  be  called  with 
each  amount.  The  word  cents  may  be  omitted  in  all  cases 
except  where  there  are  no  dollars. 

Thus,  in  calling  $400.37  sayyhwr  hundred  dollars,  thirty-seven;  in  calling 
$25.11  say  twenty-Jive  dollars,  eleven;  in  calling  $1573.86  say  fifteen  hundred 
seventy-three  dollars,  eighty-six;  in  calling  $5.31  sajfive  dollars,  thirty-one. 

WRITTEN  EXERCISE 

Write  from  dictation  and  find  the  sum  of: 

1.  $75.18,  $123.95,  $147.25,  $9.50,  $181.45,  $172.16,  $84.98, 
$314.95,  $49.10,  $69.90,  $312.60,  $415.90. 

2.  $3140.19,  $310.92,  $3164.96,  $3162.19,  $18.62,  $410.95, 
$690.18,  $10.75,  $3100.40,  $300.40,  $200.50,  $100.90,  $410.80, 
tlOO.85,  $310.60,  $80.90,  $399.80,  $412.60. 


14  CONCISE   BUSINESS   ARITHMETIC 

WRITTEN  EXERCISE 

Copy,  find  the  sum,  and  check : 

1.  2.  3. 

"f  (^  fJi^<^^Z/     "^^^  Z4^Z^^4^.f2  ^Z  /J~/  6  Z  /.^// 

yJ^cTiiyJ^.j-^    / ZJ'  f  z-/  ii\c7^  / 2  (^ z/ ^/.Cy 

3yft2Z(if./y    Z  /  y  y  ZoJ.c^  Z/3  /A^yZ.c^S 

CyZ  /  Z3^.23    y  / 3  /  A^z  C.o^  /^(^ Z  /  ^/.c^y 

A^z/z^/  z.A^s    /  z^y  z/  z.^C  f6^ry^r.c^3 

/  ZA^y  Z  /  Z.J-A^     /  3  Z  /  C^Z./  y  /  Z^ZA^y  Z.A^Z 

/  ZJ^Zf  i^A^.y  ^    Z/  A/r  y  /^  2  /.A^^  y>r^<r63r.^r 

2  / y  y  z  /  6.J~A^  3  / ^/  zs'f.c?  (^  z/A^/z<^z.^y 

^ yz 3  A^ (>y.A^r  z  /  /  A^zc? /.j-r  ry  ^yrA^y.<i / 

ZA^^^^zy.//^    3  /  y^z^y.6y  /  z  C z^yy/^ 

^£j£^;_Z^y^^^^^^^/_^  3j£/__C2_^^jyf^ 


4.  5.  6. 

^/ z  Cy  z<^/^j-  >^/  zy^Z^^.A^f'  ^/ zj-/  ^ za^.^^ 

^3y.zC  y^/  2c? A^y.y z  y z/  z  ^ ^.^^ 

/ Z.y  /  /  Z  (^  (23'^.A^Z  ^//2^^.v/4^ 

y.Cy  2/<iA//A^.yy  /j~cp^6Pc7t2.yr 

C/Zy  /^  (r6.^2  /  C  /  ^y.fz  /  y  C  y  z  /  ^.3V 

J-// /  C^.yJ'  7  2  /  A^  C.^A^  2Ayc^  /  z<2'6.zs 

y/z.yr  /  z.yj-  /  zyn3.C^ 

yz./AZ  /z^.yz  /  z<^A<yz 

<r^^.rC  z/A^C'^/  /\^/  z  <^  yz.(zy 

/ /,^6  3  2<^AZ3:y/  /  C  f  Z  /  C Z.(2A^ 

yzdf.A^z  ^2C^.(2/  /y2/.y^ 

(>y2^.y^  3(p(Z/.yr'  a^/ i^.ys 

/Zyyr./if  yj-.(pi  (^yz/.y^ 

/lA^.Ci?  /.fZ  /A^.ys 


ADDITION  15 

7.  8.  9. 

Z3  Z~y  /^./ ^  /  (i  f  Zf./^-'  /  CP  /  ^ ^ Zy.6<P 

/ZsjrCr.3^  ^y^zl/.A^z  yz/z^^^.y^^ 

zz  'yf^z.yr  /  ^ z  (^4^^j^.A^y  3  tf  fj/^^j<i 

z  C (P^JrA<f^  /^z/^j~y.fz  /f4^/yz.^j' 

zz  i!^  ^f  /.3y  yz/:zA^ ^  j./r^r  f//^f3<r.j-^ 

r3  ^ z.A^^  CfZA^/^.ZA^  /z^/z.^cp 

VZ  i^  tJ  ^.y^  ^Z./  z  (^ y.rA^  /i  A^  /  Z.yj- 

rzf^A^.33r  J  y  zf  z.zc^  /  ^  /  Cf  /  2./^z 

3 j-fA^rz.z-c?  /  z  ^ A^^.o c^  yj~/(r.fs 

yf6o:cP(p  yZA^^.<^f  /  (^ Z  /  f.yj' 

r  CJ~2  /.^<^  J  ^  c?  A^yr.4A(^  /  A^ /  yj-Z  /./Za/^ 

yjTA^j  y  /.uT^  (^  f  ^/  /  ^.j-z  /  /  z  /  A^f  o.yS 

/  (P /  6 rz3.z^  y z / zos:/ /  6f<ry^.Cz 

fZ^^^AJ./Z-  <^ Z-/ ^y  (^.dP  /  y Za^ /  J r.yj' 

A^r3  <(.f  ^  yA^ /  6  zy.  ^3  /  z  ^ A^z/,zt 

fZyr^y.A^^  C Z  /  Z-/^A^.y^  2-/ y  ZZ/.Ca^ 

ZC  2^rz.yA^  (2>y/zr.Co  CfZ/^y^ 

/  Z  (^  /  Z  f.A^J-  /  O  /  Z  <Z  /  (i.J'y  Z  /  /  /  ^fA^.JZ/ 

f  (^ rj~Z./ y  y  f  Z  ^  /  y.Zf  yyy.yA^^.^y 

/vy/z./f^  / z-/  2^  z.C (p  yZ/Z(^-y3 

Zj-  /  y  z  C.r(^  /  ^  /  A^ZyX^-  z^/  3  zy./A^ 

^ii3~3z.^^  z^/C^y.^A^  yj'yytJ.yC 

z  z  (^ / A^.yz^  Cyjyr.y^r  /  C /  z  C.^y 

V ^ z  zrA^.zo  y  (Z  /  Z-^.yZ  y  Z  / Z.a^S 

yy^^z.o^  (^yj'A^.ry  zyyzZy,/r 

C ^ ocrz.6>^  /  z  C y ^  z,^.j~A^  / <^y ZA^y.yc? 

/z<i/ZJ~.Cs  3z/6/^.yo  /^fZA^.i^yr 

3  yj-r^^A^  /J>Z3  C y. y^  Zj£j_Z^C^Z^ 


16  CONCISE   BUSINESS   ARITHMETIC 

25.  Some  accountants  practice  adding  two  columns  at  once 
when  the  columns  are  short.  The  method  generally  employed 
is  similar  to  the  method  explained  for  combining  groups  in 
regular  addition. 

26.  Example.    Find  the  sum  of  83,  72,  89.  _„ 

oo 

Solution.    Beginning  at  the  bottom  and  adding  up,  think  of  89  and  rro 

72  as  159  and  2,  or  161  ;  of  161  and  83  as  241  and  3,  or  244. 
In  adding  name  results  only.     Thus  say  159,  161,  241,  24Ji^ 


89 
244 


ORAL  EXERCISE 

By  inspection  give  the  sum  of  each  of  the  folloiving  groups : 
1.       2.       3.        4.       5.       6.       7.       8.       9.     10.    11.    12.     13.    14.    15. 

43  64  52  37  65  38  52  85  93  68  58  76  83  57  62 
251829562743673472754639472539 

16.     17.     18.      19.     20.     21.     22.    23.    24.    25.    26.    27.    28.    29.    30. 

53  52  61  34  91  68  48  24  78  54  94  57  92  76  43 
4643     37     761347699676353644373156 

31.    32.    33.    34.    35.     36.    37.    38.    39.     40.     41.     42.     43.     44.     45. 

65  44  46  48  67  44  53  25  54  46  33  16  67  83  88 
86  57  Qb  25  48  57  45  31  65  39  64  34  43  82  25 
75213431392167698787^25419831 

HORIZONTAL  ADDITION 

27.  In  some  kinds  of  invoicing  and  in  short-extending  the 
items  of  an  account  numbers  to  be  added  are  written  in  horizon- 
tal lines.  Much  time  may  be  saved  by  adding  these  numbers 
as  they  stand.  After  careful  practice  it  will  be  found  possible 
to  add  numbers  written  in  horizontal  lines  with  as  much 
facility  as  numbers  written  in  vertical  columns. 

28.  In  adding  numbers  written  horizontally  care  should  be 
exercised  to  combine  only  units  of  the  same  order.  It  is  gener- 
ally best  to  add  from  left  to  right  and  to  verify  the  work  from 
right  to  left.  Grouping  may  be  employed  to  advantage  in 
horizontal  addition. 


ADDITION  17 

WRITTEN  EXERCISE 

Copy  and  add  the  following  numhers  horizontally.  Verify  the 
work. 

Thus,  in  problem  1,  beginning  at  the  left,  say  10^  20,  32,  52.  In  verifying 
the  work  from  the  right  say  20,  32,  42,  52. 

1.  8,2,1,1,7,1,4,6,2,3,8,9. 

2.  7,  9,  6,  5,  4,  8,  7,  4,  3,  7,  3,  1,  3. 

3.  6,  2,  4,  8,  3,  1,  7,  6,  4,  2,  8,  9,  4,  2. 

4.  15,  23,  46,  83,  29,  35,  42,  15,  21,  26. 

5.  64,  48,  m,  35,  47,  87,  32,  45,  67,  91. 

6.  52,  64,  86,  28,  76,  41,  15,  32,  12,  87. 

7.  32,  48,  24,  62,  85, 14,  63,  54,  78,  94,  23,  45. 

8.  42,  76,  49,  81,  17,  42,  17,  19,  21,  43,  64, 17. 

9.  45,  48,  34,  46,  48,  53,  25,  42,  35,  56,  70,  10. 

10.  291,  196,  855,  578,  210,  354,  102,  232,  241,  162. 

11.  469,  388,  962,  764,  351,  899,  111,  232,  190,  175. 

12.  1525,  5025^  1684,  3142^  ggss^  igw  2312,  iQis,  6480,  4010. 

It  is  frequently  desirable  to  express  dollars  and  cents  without  the  dollar 
sign  and  the  decimal  point.  This  may  be  done  by  slightly  raising  the  cents 
of  the  amount.     Thus,  $  17.17  may  be  written  17" ;  ^  2.08  may  be  written  2«8. 

13.  1525,  893,  488,  2184,  1635^  1846,  291*,  44^0,  6290,  8460,  4050. 

14.  76'5,  8497,  6705,  9574^  6863,  5221,  1325^  4218,  6095,  80i3,  90^2. 

29.  It  is  important  that  the  student  acquire  the  ability  to 
carry  a  series  of  numbers  in  mind.  The  following  exercises 
are  suggestive  of  what  may  be  done  to  cultivate  ability  in  this 
direction. 

The  dictation  suggested  should  not  be  slower  than  at  the  rate  of  one  . 
hundred  twenty  words  per  minute.  Nothing  should  be  written  by  the 
students  until  all  of  the  numbers  of  a  problem  have  been  called  by  the 
instructor;  then  one  student  may  be  sent  to  the  blackboard  and  required 
to  write  the  numbers  from  memory.  If  the  numbers  are  correctly  written, 
the  instructor  may  require  another  student  to  give  the  sum  of  them  with- 
out using  pen  or  pencil.  The  numbers  may  be  written  on  the  board  in 
either  vertical  or  horizontal  order,  as  the  instructor  may  direct. 


18 


CONCISE   BUSINESS   ARITHMETIC 


ORAL  EXERCISE 


From  the  instructor's  dictation  find  mentally  the  sum  of  each  of 
the  following  problems  : 


1.  6,  9,  8,  4,  8,  6.  15. 

2.  14,  17,  20,  5,  9.  16. 

3.  24,  17,  16,  9,  5.  17. 

4.  5,  6,  7,  1,  3,  8.  18. 

5.  6,  2,  8,  1,  7,  4.  19. 

6.  364,  436,  657,  25.  20. 

7.  438,  212,  750,  64.  21. 

8.  859,  441,  769,  71.  22. 

9.  2140,  3160,  4000.  23. 

10.  200,  415,  600,  95.  24. 

11.  857,  643,  237,  500.  25. 

12.  S  4150,  $4050,  $850.  26. 

13.  $5.15,  $2.15,  $6.70.  27. 

14.  $167.14,  $232.86,  $9.  28. 


147,  253,  179,  121. 
423,  517,  81,  49. 
255,  45,  89,  121. 
25,  65,  27,  133. 
$48,  $32,  $138. 
$135,  $275,  $418. 
$23,  $67,  $281. 
$284,  $36,  $245. 
133,  167,  29,  61. 
2319,  1681,  2335. 
3310,  2790,  1565. 
2740,  1365,  2135. 
2273,  1237,  1145. 
1432,  1058,  1210. 


WRITTEN  REVIEW  EXERCISE 

1.  Find  the  sum  of  all  the  integers  from  2165  to  2260  inclu- 
sive. 

2.  Find  the  sum  of  all  the  integers  froin  1137  to  1200  inclu- 
sive. 

3.  Complete  the  following  sales  sheet.  Add  by  columns 
and  by  lines  and  check  the  work  by  adding  the  vertical  and 
horizontal  totals. 

Summary  of   Sales   for   Week  Ending    Aug.   25 


ADDITION 


19 


4.    Add  the  following  by  columns  and  by  lines,  and  check 
the  work  by  adding  the  vertical  and  horizontal  totals  : 


21162 

49 

962 

18 

1245 

76 

54168 

97 

52 

19 

176 

19 

1278 

95 

52698 

13 

7529 

87 

95162 

87 

2164 

89 

7524 

16 

47612 

87 

6842 

23 

6948 

23 

76 

95 

87 

14 

2150 

49 

172 

93 

1745 

86 

51276 

92 

18187 

95 

75 

19 

162 

14 

5290 

18 

9834 

18 

92923 

15 

25 

91 

162 

18 

14 

95 

754 

95 

2167 

92 

2584 

16 

9176 

92 

3164 

82 

1356 

05 

1314 

93 

7125 

95 

2167 

18 

2645 

97 

756 

92 

142 

18 

167 

42 

926 

44 

3167 

18 

75162 

19 

82195 

78 

72162 

18 

9165 

97 

168 

44 

7162 

95 

4167 

18 

7156 

95 

172 

18 

1 

56 

2 

15 

6843 

82 

3954 

05 

60 

65 

9 

18 

8 

85 

9162 

19 

5144 

65 

8162 

18 

91684 

57 

2416 

45 

1829 

32 

4217 

64 

1492 

95 

8647 

64 

168 

94 

257 

16 

417 

86 

952 

17 

347 

18 

,  5.  Complete  the  following  sales  sheet.  Add  by  columns 
and  by  lines  and  then  check  the  work  by  adding  the  vertical 
and  horizontal  totals. 


Summary  op  Clerks'   Daily  Sales 


Names  of  Cleeks 

Monday 

TtTESDAY 

Wednesday 

Thuesday 

Feiday 

Satuedat 

Total 
FOE  Week 

J.  E.  Snow 

167 

18 

194 

67 

98 

46 

241 

80 

175 

66 

314 

90 

W.  B.  Moore 

78 

20 

65 

14 

50 

42 

60 

93 

61 

19 

64 

86 

T.  B.  Welch 

112 

40 

118 

64 

192 

40 

146 

18 

110 

50 

140 

12 

E.  H.  Ross 

164 

90 

143 

18 

192 

64 

214 

10 

110 

60 

190 

18 

Minnie  Davis 

165 

19 

214 

78 

120 

42 

167 

18 

164 

27 

140 

51 

Ada  Benton 

68 

49 

90 

81 

64 

75 

120 

14 

142 

16 

60 

90 

Elmer  S.  Frey 

240 

18 

920 

41 

718 

52 

167 

59 

840 

72 

143 

86 

Joseph  White 

22 

49 

72 

86 

51 

47 

62 

14 

91 

26 

72 

15 

Margaret  Dix 

47 

26 

91 

18 

21 

64 

18 

42 

61 

19 

64 

86 

F.  0.  Beck 

127 

16 

95 

27 

114 

82 

162 

15 

102 

15 

112 

61 

L.  0.  Avery 

214 

91 

218 

46 

920 

41 

172 

14 

155 

86 

142 

71 

B.  W.  Snyder 

162 

14 

153 

46 

118 

64 

162 

14 

182 

15 

69 

58 

Ella  Harding 

21 

27 

18 

92 

17 

65 

28 

64 

59 

18 

72 

41 

Carrie  Simpson 

21 

18 

45 

30 

16 

98 

42 

41 

20 

68 

75 

98 

W.  F.  Baldwin 

162 

10 

114 

80 

115 

00 

116 

84 

117  411 

200 

60 

E.  0.  Burrill 

84 

90 

90 

10 

116 

80 

114 

30 

65 

20 

300 

75 

Total 

6.    On  the  page  following  are  a  number  of  inventory  exten- 
sions ;  find  the  footing  of  each. 


20  CONCISE   BUSINESS   AEITHMETIC 

Each  column  should  be  added  in  approximately  three  minutes. 


a. 

I. 

c. 

d. 

$1628.45 

$1743.19 

$2065.32 

$1156.78 

176.22 

78.91 

145.55 

11.69 

453.26 

1011.45 

28.49 

189.24 

1102.65 

125.60 

217.86 

338.54 

45.22 

101.25 

207.41 

24.75 

143.51 

74.24 

1078.44 

8.95 

55.68 

212.35 

45.60 

1250.05 

425.70 

338.90 

256.85 

74.33 

119.45 

227.83 

194.61 

258.97 

7.15 

46.21 

112.45 

364.20 

89.52 

117.25 

34.65 

126.70 

48.75 

57.81 

133.27 

82.56 

170.25 

9.11 

24.13 

219.63 

613.81 

764.35 

495.34 

360.42 

1203.05 

88.75 

6.17 

24.45 

327.16 

401.19 

98.75 

175.26 

654.32 

1145.22 

856.21 

1364.12 

108.17 

366.18 

1408.95 

374.11 

75.45 

201.13 

376.23 

211.06 

9.58 

64.33 

112.50 

21.08 

142.53 

8.78 

56.40 

312.74 

189.70 

89.56 

76.50 

118.44 

20.65 

192.35 

244.56 

94.65 

673.13 

98.75 

339.54 

951.15 

120.06 

320.16 

87.40 

73.07 

65.34 

135.20 

467.80 

239.15 

753.25 

■    846.18 

515.05 

1856.22 

371.10 

1904.76 

287.01 

475.02 

69.16 

128.44 

301.04 

602.13 

231.06 

473.08 

1654.23 

342.50 

503.44 

95.16 

270.15 

89.65 

78.42 

143.65 

69.40 

439.20 

250.21 

54.30 

355.11 

175.06 

2859.89 

1756.84 

742.13 

1914.56 

ADBITIOK  21 

WRITTEN   EXERCISE 

Each  of  these  groups  should  be  added  in  approximately  one  minute. 

1.                                                   2.  3. 

6,354,276,742  6,917,408,583  8,632,714,509 

5,116,433,854  5,880,734,112  6,875,352,272 

8,446,750,284  6,538,922,553  8,539,168,753 

2,141,991,648  7,543,276,445  8,335,674,912 

4.653.752.816  6,441,819,263  5,321,841,174 

3.256.851.539  2,574,438,911  2,435,627,819 

5.462.175.255  4,156,717,549  1,546,721,973 
6,435,621,953  1,817,908,667  5,167,534,217 
4,717,880,945  6,745,243,517  4,576,819,054 
5,601,523,764  3,546,798,212  4,151,762,492 

4.                                                   5.  6. 

2,334,515,637  5,432,317,892  6,453,615,809 

5.734.516.772  6,534,317,865  4,576,879,253 

7.354.618.227  4,531,841,962  2,432,653,274 
3,542,618,906  3,132,341,264  7,819,457,836 
5,115,616,874  4,651,272,335  '  1,918,776,425 

7.175.437.256  3,256,728,143  5,327,731,224 

1.735.273.540  1,830,925,165  4,532,551,243 

8.134.556.773  2,543,175,213  6,231,605,228 
3,115,617,221  3,413,214,605  7,615,257,818 
3,255,617,711  5,443,216,448  5,663,338,119 

7.                                                   8.  9. 

4.334.561.228  3,653,212,716  4,176,234,562 
1,765,371,442  7,661,823,394  5,934,736,548 
9,717,632,461  5,749,287,716  6,254,817,259 
5,616,727,640  3,264,723,445  1,218,735,143 

2.615.431.817  2,845,367,621  7,342,235,907 
4,256,713,332  4,256,443,486  6,543,217,194 
3,078,395,668  7,254,563,823  2,546,718,911 
7,845,446,772  9,117,224,383  3,664,293,189 
8,250,114,337  1,493,786,332  9,226,847,821 


22  CONCISE   BCrSlKESS   AKITHMETIC 

A  WRITTEN  REVIEW  TEST 

Write  the  following  problems  from  dictation^  and  tTien  complete 
the  work.  Time,  approximately^  thirty  minutes,  including  the  dicta- 
tion.   Add  the  following  : 

1.  2. 

23,418     17,546         28,356  43,572 

43,621      23,811         32,718  21,471 

71,892      32,264         10,918  37,509 

22,457     31,542         27,354  42,311 

34,256      45,623         45,612  20,175 

41,243      54,819         33,452  75,604 

44,172      22,716         31,174  70,219 

34,523     45,613         44,530  28,332 

31,113     41,414         45,517  37,743 

20,125     13,064         50,197  22,508 

62,157     93,845         29,875  45,612 


In  problems  3  and  4  add  by  columns  and  then  by  lines,  and  check 
the  work  by  adding  the  vertical  and  horizontal  totals. 


542 

236 

? 

123 

235 

? 

437 

653 

? 

947 

834 

? 

572 

246 

? 

174 

215 

? 

445 

354 

? 

313 

208 

? 

236 

716 

? 

364 

312 

? 

423 

394 

? 

252 

733 

? 

347 

616 

? 

243 

317 

? 

455 

494 

? 

203 

406 

? 

337 

651 

? 

543 

392 

? 

453 

283 

? 

527 

618 

? 

624 

912 

? 

624 

483 

? 

538 

496 

? 

713 

626 

? 

712 

324 

? 

235 

439 

? 

? 

? 

? 

? 

? 

? 

CHAPTER  III 

SUBTRACTION 
ORAL  EXERCISE 

State  the  number  that^  added  to  the  smaller  number^  makes  the 
larger  07ie  in  each  of  the  following : 

1.      344567889999887 


1 

2 

1 

3 

2 

3 

3 

2 

3 

1 

6 

4 

4 

1 

2 

2. 

12 

11 

12 

11 

12 

11 

12 

11 

10 

11 

10 

11 

10 

12 

10 

_9 

2 

3 

9 

8 

3 

4 

_8 

4 

_7 

6 

4 

7 

5 

3 

3. 

18 

17 

16 

17 

16 

15 

14 

15 

14 

13 

13 

16 

15 

14 

13 

9 

8 

7 

9 

8 

6 

9 

7 

8 

4 

j; 

9 

8 

5 

9 

4. 

13 

14 

14 

15 

16 

17 

18 

18 

19 

19 

19 

19 

18 

18 

17 

11 

12 

11 

13 

12 

13 

13 

12 

13 

11 

16 

14 

14 

11 

12 

5. 

22 

21 

22 

21 

22 

21 

22 

21 

20 

21 

20 

21 

20 

22 

20 

19 

12 

13 

19 

18 

13 

14 

18 

14 

17 

16 

14 

17 

15 

13 

6. 

38 

27 

26 

37 

26 

35 

44 

25 

34 

53 

43 

36 

45 

54 

73 

29 

18 

17 

29 

18 

26 

39 

17 

28 

44 

37 

29 

38 

45 

69 

7. 

42 

51 

72 

81 

92 

71 

32 

41 

70 

61 

90 

81 

30 

62 

50 

39 

42 

63 

79 

88 

63 

24 

38 

64 

57 

86 

74 

27 

55 

47 

30.    A  parenthesis  (  )  signifies  that  the  numbers  included 
within  it  are  to  be  considered  together.     A  vinculum  has 

the  same  signification  as  a  parenthesis. 


Thus,  15-  (4  +  2),  or  15-4  +  2  signifies  that  the  sum  of  4  and  2  is  to 
be  subtracted  from  15. 

23 


24 


CONCISE   BUSINESS   ARITHMETIC 


31.   Examples,    l.    Find  the  difference  between  849  and  162. 


Solution.    2  from  9  leaves  7.     6 cannot  be  subtracted  from  4,  but  6       qaq 
from  14  leaves  8.    Since  1  of  the  8  hundreds  has  been  taken,  there  are  but       -|  /»n 

7  hundreds  remaining.     1  from  7  leaves  6.  

Check.     687  +  162  =  849.  687 

The  above  is  a  common  method  of  subtraction.     For  practical  computation, 

however,  the  "making  change"  method  is  best.     It  is  easily  understood  and 

is  much  more  rapid  when  once  learned.     The  "making  change"  method  is 

illustrated  in  the  following  example  and  solution. 

2.    Find  the  difference  between  7246  and  4824. 

Solution.     Think    "4  +  2  =6,"  and  write  2;    "2  +  2  =  4,"  and       7246 

write  2  ;  "  8  +  4  =  12,"  and  write  4  j  "  1  and  4  +  2  =  7,"  and  write  2.      4824 

Check.    2422  +  4824  =  7246.  •  "2422 


ORAL  EXERCISE 


1.  16+  23  +  ?  =  54?  7. 

2.  27  +  14  +  ?=72?  8. 

3.  17 +  36  +  ?  =62?  9. 

4.  19 +  17 +  12  +  ?  =57?  10. 

5.  25 +  14 +  11+?  =  75?  11. 

6.  18  +  17  +  16  +  ?  =  70?  12. 


16  +  18  +  16=25  +  ? 
72  +  17  +  11  =  37  +  ? 

14  +  18  +  38  =  42  +  ? 
12  +  16  +  12  +  14+?: 


75? 


16 +  15 +  19 +  15+?  =  93? 
18 +  17 +  15 +  29+?  =  98? 


WRITTEN  EXERCISE 

1.   Without  copying   the   individual  problems,  find  quickly 
the  sum  of  the  twenty  differences  in  the  following: 


12140.50 

$4157.50 

$5000.24 

$9000.72 

$3145.62 

714.23 

1236.80 

249.17 

1246.18 

2000.79 

$5500.89 

$1624.14 

$1985.72 

$1379.54  - 

$1742.18 

2799.14 

957.80 

645.92 

923.18 

842.16 

19275.17 

$2446.80 

$3169.14 

$3156.19 

$4756.83 

842.99 

1321.44 

874.36 

1400.72 

2738.44 

17514.85 

$7291.80 

$1756.92 

$8721.13 

$1872.14 

721.92 

1642.95 

•921.74 

2049.79 

742.12 

SUBTRACTION 


25 


2.  Copy  the  following  table  and  show  (a)  the  total  exports 
for  each  year  given;  (5)  the  excess  of  exports  for  each  year 
given ;  (tf)  the  total  exports  and  imports  for  the  ten  years ; 
(c?)  the  total  excess  -of  exports  for  the  ten  years.     Check. 

Imports  axd  Exports  ix  the  United  States  for  Ten  Years 


Year  End- 

Exports 

Total 
Exports 

Imports 

Excess  of 

ixu  June  30 

Exports 

Domestic 

Foreign 

1904 

$1435170  017 

$25  648  254 

.$991090  978 

1905 

1  491  744  641 

26  817  025 

1117  513  071 

1906 

1  717  953  382 

25  911 118 

1  226  562  446 

1907 

1  853  718  034 

27  133  044 

1  434  421  425 

1908 

1  834  786  357 

25  986  357 

1 194  341  792 

1909 

1  638  355  593 

24  655  51i 

1311920  224 

1910 

1  710  083  998 

34  900  722 

1556  947  430 

1911 

2  013  549  025 

35  771  174 

1  527  226  105 

1912 

2  170  319  828 

34  002  581 

1  653  264  934 

1913 

2  428  506  358 

37  377  791 

1  812  978  234 

Total 

Under  the  term  domestic  exports  are  included  exports  of  merchandise, 
the  growth,  produce,  or  manufacture  of  the  United  States ;  under  foreign 
exports  are  included  articles  of  merchandise  previously  imported  into  the 
United  States  and  subsequently  reexported.  Under  the  term  imports  are 
included  imports  of  all  merchandise  of  whatever  origin  received  into  the 
United  States. 

32.  The  common  method  of  making  change  is  to  add  to  the 
price  of  the  goods  purchased  a  sum  that  will  equal  the  amount 
offered  in  payment. 

Thus,  if  a  person  buys  groceries  amounting  to  7^^  and  tenders  $1  in 
payment,  the  mental  process  of  the  clerk  in  making  the  change  is  as  follows : 
"74^2^  +  1/^  +  25jz^  =  $1";  the  customer  should  receive  as  change  a  1-cent 
piece  and  a  quarter  of  a  dollar. 

Change  may  be  made  in  a  number  of  ways.  In  the  above  example  two 
dimes  and  a  5-cent  piece  might  be  given  instead  of  the  quarter  of  a  dollar. 
In  the  following  exercise  name  the  largest  coins  and  bills  that  could  be  used. 

ORAL  EXERCISE 

1.  Name  the  coins  and  the  amount  of  change  to  be  given 
from  S 1  for  each  of  the  following  purchases :  17/;  24/;  31/; 
38/;  45/;   52/;  59/;   m  pf ',  73/;  80/;  87/;  18/;   25/. 


26  COKCISE   BUSINESS   ARITHMETIC 

2.  Name  the  coins  and  the  amount  of  change  to  be  given 
from  $2  for  each  of  the  following  purchases:  11.19;  f  1.26 

$1.33;  $1.40;  $1.47;  $1.54;  $1.61;  $1.68;  $1.75;  $1.82 
$1.89;  $1.20;  $1.27;  $1.34;  $1.41;  $1.48;  $1.55;  $1.62 
$1.69;  $1.76;  $1.83;  $1.90. 

3.  Name  the  bills  and  coins  and  the  amount  of  change  to  be 
given  from  $5  for  each  of   the  following   purchases:    $1.21 
$1.28;  $1.35.;  $1.42;  $2.22;   $2.29;   $2.36;   $4.43;  $3.49 
$4.50;  $3.51;  $3.56;  $4.57;  $2.58;  $1.63;  $2.64;  $1.65 
$1.70;  $2.71;  $3,72;  $2.77;  $3.84;  $1.91;  $2.85;   $2.92. 

4.  Name  the  bills  and  coins  and  the  amount  of  change  to  be 
given  from  $10  for  each  of  the  following  purchases:   $4.93 


$3.23;  $5.17;  $4.24 

$3.66;  $5.73;  $4.80 

$3.60;  $4.53;  $2.46 

$9.42;  $3.67;  $1.93. 


$3.86;  $7.70;  $2.44;  $8.37;  $5.30 

$3.31;  $8.38;  $2.45;  $6.52;  $4.59 

$3.87;  $2.88;  $7.81;  $9.74;  $5.67 

$3.29;  $8.32;  $7.25;  $2.18;  $7.49 

33.  It  is  frequently  necessary  to  find  the  difference  between 
a  minuend  and  several  subtrahends.  If  the  "  making  change  " 
method  of  subtraction  is  employed,  the  operation  is  a  simple 
one. 

34.  Example.  From  a  farm  of  578  A.  I  sold  at  one  time  162 
A.,  at  another  98  A.,  and  at  another  121  A.  How  many  acres 
remained  unsold  ? 

rrTQ      A 

Solution.     Arrange  the  numbers  as  shown  in  the  margin.  Dio  ^. 

Eleven  (1  +  8  +  2)  and  seven  are  18  ;  write  7.     Three  (1  carried  162  A. 

+  2),  eighteen  (3  +  9  +  6)  and  nine  are  twenty-seven;  write  9.  gg 

Four  (2  carried  +  1  +  1)  and  one  are  6  ;  write  1.  121 

Check.     197  +  121  +  98  +  162  =  678. 


197  A. 


WRITTEN  EXERCISE 

Find  the  amount  each  person  has  remaining  on  deposit: 

1.  A.    Deposit,  1900;  checks,  1210,  $175,  $198. 

2.  B.    Deposit,  $875;  checks,  $157,  $218,  $157. 

3.  C.    Deposit,  $750;  checks,  $120,  $117,  $121,  $118. 

4.  D.    Deposit,  $960;  checks,  $128,  $109,  $118,  $117. 


SUBTRACTION 


27 


5.  E.    Deposit,  $967;  checks,  $192, 1102,  |11T,  $128,1146. 

6.  F.    Deposit,  1998;  checks,  $119,  $117, 1105,  $123,1173. 

Do  not  neglect  to  check  all  work.  The  bank  clerk  who  makes  an  error 
a  day  in  work  like  the  above,  and  who  fails  to  discover  and  correct  this 
error,  will  not  long  retain  his  position. 

7.  Copy  the  following,  supplying  the  missing  terms  and 
checking  the  results  : 

$148.90  +  $149.75  +  $421.77  = 
118.60+  172.12+  ???.??  = 
242.30+  ???.??+  210.96  = 
???.??+     168.72+     130.41  = 


?  ?  ? 

?  ?  ? 

?  ?  ? 

?  ?  9 


?  ? 
?? 

?? 
?  ? 


9  ? 


$718.95  +  $698.75  +  $978.60  =$??  ?  ?. 

The  following  problem  shows  a  portion  of  a  bank  discount  register.  In 
the  first  column  are  recorded  the  amounts  of  several  notes  that  have  been  dis- 
counted ;  in  the  second,  the  discount  charges ;  and  in  the  third,  the  collection 
and  exchange  charges.  The  proceeds  of  any  note  is  the  difference  between 
the  amount  (face)  of  the  note  and  the  total  charges  upon  it. 

8.  Copy  and  complete  the  following  bank  record.  Check 
the  work.     (/  +  z  +  A  should  equal  g.) 


Face  of  Paper 

Discount 

Coll.  &  Excu. 

Proceeds 

729 

U 

7 

29 

73 

a 

862 

29 

4 

31 

86 

b 

725 

74 

7 

26 

73 

c 

832 

16 

12 

48 

1 

26 

d 

426 

19 

6 

39 

43 

e 

378 

36 

3 

78 

38 

f 

9 

h 

i 

J 

35.  The  complement  of  a  number  is  the  difference  between 
the  number  and  a  unit  of  the  next  higher  order. 

Thus,  2  is  the  complement  of  8,  23  is  the  complement  of  77,  and  152  is 
the  complement  of  848.  3  and  7,  24  and  76,  250  and  750,  are  complementary 
numbers.  Observe  that  when  two  numbers  of  more  than  one  figure  each  are 
complementary,  the  sum  of  the  units*  figure  is  10  and  the  sum  of  the  figures  in 
each  corresponding  higher  order  is  9. 

CB 


28  CONCISE   BUSINESS   ARITHMETIC 

36.  Since  numbers  are  read  from  left  to  right,  in  finding  the 
complement  of  a  number,  begin  at  the  left  to  subtract. 

37.  In  beginning  at  the  left  to  subtract  take  1  from  the 
highest  order  in  the  minuend  and  regard  the  other  orders  as 
9's,  except  the  last,  which  regard  as  10. 

38.  Example.  A  man  gave  a  100-dollar  bill  in  payment  for 
an  account  of  $77.52.     How  much  change  should  he  receive  ? 

Solutions,  (a)  Begin  at  the  left.  7  from  9  leaves  2;  7  from  9  f  100.00 
leaves  2  ;  5  from  9  leaves  4 ;  2  from  10  leaves  8.     Or  77  ^9 

(b)   7  and  2  are  9 ;  7  and  2  are  9  ;   6  and  4  are  9  ;  2  and  8  are  ' 

10.     $22.48.  $22.48 

This  method  of  finding  the  amount  of  change  is  used  by  many  clerks  and 
cashiers.  The  work  is  in  all  cases  proved  by  counting  out  to  the  customer 
the  bills  and  coins  necessary  to  make  the  amount  of  the  purchase  equal  to 
the  amount  offered  in  payment. 

ORAL  EXERCISE 

Find  the  total  of  each  group  of  numbers,  then  find  the  difference 
between  the  two  totals: 

1.  (24  26  32  30  35  25)  -  (18  13  19  12  20  30). 

2.  (13  27  45  25  21  19)  -  (15  14  21  32  18  22). 

3.  (11  29  35  15  24  16)  -  (27  13  18  22  25  20). 

4.  (17  14  29  32  22  26)  -  (23  13  16  24  20  16). 

5.  (45  25  30  40  32  18)  -  (25  35  33  17  20  30). 

6.  (34  24  35  30  15  32)  -  (21  39  14  15  11  30). 

7.  (15  25  33  27  14  36)  -  (13  30  16  14  20  16). 

8.  (14  16  30  10  40  50)  -  (11  19  18  12  20  30). 

9.  (19  10  11  20  30  32)  -  (15  11  14  30  32  18). 
,10.  (33  17  22  11  17  50)  -  (21  19  31  12  17  40). 

11.  (25  30  15  40  15  20)  -  (15  16  19  21  29  30). 

12.  (17  23  25  26  15  44)  -  (24  20  26  27  13  20). 

13.  (11  39  52  18  10  20)  -  (12  18  40  22  28  12). 

14.  (35  15  27  23  34  16)  -  (21  17  12  42  13  15). 

15.  (22  18  34  26  60  10)  -  (35  15  20  11  19  31). 

16.  (33  17  22  18  40  60)  -  (14  26  23  17  40  12). 


SUBTEACTION 

29 

ORAL  EXERCISE 

State  the  amount 

of  change  in 

each  of  the  following  problems : 

Cost  of 

Amount 

Cost  of 

Amount 

Items  Purchased 

Paid 

Items  Purchased 

Paid 

1. 

17^,  13^,  42^ 

12 

14. 

11.25,    $0.75,  $2.18 

$20 

2. 

27^,  23^,  14^ 

12 

15. 

il.50,    12.70,11.18 

$20 

3. 

45^,  55^,  13^ 

15 

16. 

$4.60,    $1.40,  $2.13 

$20 

4. 

64^,  16^,  87^ 

15 

17. 

$1.50,    $1.20,  $2.30 

$10 

5. 

23^,  14^,  27^ 

$2 

18. 

$3.17,    $4.11,14.98 

$50 

6. 

63.^,  17^,  59iZf 

$5 

19. 

$4.25,    $0.75,  $3.18 

$20 

7. 

49^,  84^,  37^ 

f5 

20. 

$1.29,    $2.17,  $1.50 

$20 

8. 

78^,  42^,  67^ 

$5 

21. 

$1.64,    $1.66,  $2.50 

$20 

9. 

52^,  69^,  885^ 

15 

22. 

$1.59,  $23.41,   $118 

$200 

10. 

75^,  86^,  54^ 

15 

23. 

$24.17,  $20.83,     $15 

$100 

11. 

89^,  46^,  72^ 

15 

24. 

$11.48,  $10.52,     $50 

$100 

12. 

76^,  54^,  29^ 

$5 

25. 

$18.91,  $12.09,     $45 

$100 

13. 

75^,  25^,  89^ 

810 

26. 

$21.27,  $2.73,  $50.50 

$100 

39.  19  —  7  =  9  (the  minuend  minus  10)  +  3  (the  comple- 
ment of  the  subtrahend);  191  —  17  =  91  (the  minuend  minus 
100)  +  83  (the  complement  of  the  subtrahend)  ;  1912  -  178  = 
912  (the  minuend  minus  1000)  4-  822  (the  complement  of  the 
subtrahend),  and  so  on. 

40.  This  principle  makes  it  a  simple  matter  to  find  the  dif- 
ference between  a  subtrahend  and  several  minuends. 

41.  Examples.  The  following  examples  illustrate  the  appli- 
cation of  the  principle : 

Solutions.    1.   2  (the  complement  of  8),  i,  2.  3. 

10,  16;  16  — 10  =  6.  9  (the  complement  of  1),         gig  299  311 

16,  17;  17-10  =  7.     9,  13,  16;  16-10=6. 

2.  9,  17,  26;  26-10=16;  that  is,  6  and  1  +-*<Q  +^^Q  +^^^ 
to  add  to  the  minuends.  9,  18  (9+8  +  1),  27;  —118  —111  —219 
27-10  =  17;  that  is,  7  and  1  to  add  to  the  =676  =676  =203 
minuends.     9,  14,  16;  16-10=6. 

3,  1,  2,  3.  3  —  10  is  impossible,  so  subtract  1  ten  from  the  minuend  (or  add 
1  ten  to  the  subtrahend).     9,  10.     10-10  =  0.     8,  9,  12.  12-10  =  2. 


30 


CONCISE   BUSINESS   ARITHMETIC 


42.   Example.   The  following  problem  shows  a  concrete  appli- 
cation of  the  foregoing  principle  : 

Depositors'  Ledger 


Solution.  Here  is  a 
depositors'  ledger.  TJie 
data  in  the  first  three 
columns  being  given,  it 
is  required  to  find  the 
new  balance. 


Depositor 

Balance 

Checks 

Deposits 

A 
B 
C 

^74 
$86 
192 

$25 
$11 
$79 

$86 
$99 
$81 

Balance 

$135 

$174 
$    94 


The  process  is  as  follows:    A.  6,  11,  15,  5;   8,  16,  23,  13;  balance,  $135. 

B.  9,  18,  24,  4  and  1  to  add  to  the  minuend.     10,  19,  27,  17;  balance,  $174. 

C.  1,  2,  4  and  1  to  take  away  from  the  minuend.     7,  10,  19,  9;  balance,  $94. 

WRITTEN  EXERCISE 

Find  the  new  balances^  the  total  old  balance^  the  total  checks^  the 
total  deposits^  the  total  new  balances^  and  cheek  the  work: 

1.  2. 


Dbpositok 

Bal. 

Checks 

Deposits 

Bal. 

A 

$758 

$128 

$  421 

a 

B 

921 

154 

175 

h 

c 

934 

214 

122 

c 

D 

862 

162 

218 

d 

E 

478 

187 

126 

e 

F 

921 

215 

124 

f 

G 

756 

157 

137 

9 

H 

864 

128 

142 

h 

I 

926 

214 

121 

i 

J 

752 

221 

124 

J 

K 

878 

162 

218 

k 

/ 

m 

n 

0 

Depositor 

Bal. 

Checks 

Deposits 

Bal. 

A 

$428 

$125 

$  718 

a. 

B 

726 

128 

296 

h 

C 

832 

279 

318 

c 

D 

456 

154 

421 

d 

E 

298 

275 

568 

e 

F 

728 

178 

188 

f 

G 

762 

218 

215 

9 

H 

837 

316 

176 

h 

I 

493 

121 

219 

i 

J 

862 

128 

188 

J 

K 

925 

125 

211 

k 

I 

m 

n 

0 

43.  48  —  29  =  48  +  1  (30,  the  next  higher  order  of  units  than 
29,  -  29)  -  30,  or  19 ;  128  -  59  =  128 -f- 1  -  60,  or  69. 

44.  This  principle  may  be  applied  to  advantage  in  billing 
items  in  which  the  gross  weights  and  the  tares  are  recorded. 

The  gross  weight  is  the  weight  of  merchandise,  together  with  bag,  cask, 
or  other  covering ;  the  tare  is  the  weight  of  the  bag,  cask,  or  other  covering 


SUBTEACTION 


31 


of  merchandise ;  the  net  weight  is  the  difference  between  the  gross  weight 
and  the  tare. 

45.  Example.  The  gross  weights  and  tares,  in  pounds,  of  3  bbl. 
of  sugar  are :  332  -  19,  337-18,  335  - 18.  Find  the  total  net 
weight. 


332-19     337-18    335-18    949  # 


Solution.  The  numbers 
would  be  written  on  the  bill 
horizontally,  as  shown  in  the  margin.  Adding  the  units  of  the  tare,  the  result 
is  25  ;  30  (the  next  higher  order  of  units  than  25)  minus  25  equals  5  ;  5  added 
to  the  units  of  the  gross  weight  equals  19 ;  19  —  30  is  impossible,  so  write  9 
and  subtract  2  tens  (the  difference  between  the  tens  in  30  and  19)  from  the 
gross  weight  or  add  2  tens  to  the  tens  of  the  tare.  Adding  2  tens  to  the  tens 
of  the  tare,  the  result  is  5  ;  10  —  5  =  5 ;  5  added  to  the  tens  of  the  gross  weight 
equals  14 ;  14  —  10  =  4.  Adding  the  hundreds  in  the  gross  weight,  the  result 
is  9.     Net  weight  is  949  lb. 


WRITTEN  EXERCISE 


Oofy  the  following  hills.     Verify  the  net  weights  given  and  supply 
all  missing  terms. 


1. 

Chicago,  III 


'.-^^^/Z, 


yi(r.<i,<i^r<^. 


JO. 


Bought  of  PHIUP  ARMOUR  &  CO. 


Terms 


J/t/^^l^^-d^^^^^^'-r^ 


7<?-  /'^ 


—  /^4-      y/-/^ 


lA^ <±t 


J^ 


A. 


^^>^- 


7^^^^Z^^>^^^^^^^,^ 


^J.2.-C^     VZf-70      ^Z^-  C<J- 

^2.^-/:^    z^^.^-v^    A^z^-ya 2.AJLL — 'Jtl 


^il 


7^-L^^^  ry^A;-7.^'2^y^  ^^ 


H4- 


7^ 


U»X>--7n       </i/2.-'T/       ^/^-«^^ 


»***■       ^^^  3 oj 


2A 


JUL 


32 


CONCISE  BUSINESS   ARITHMETIC 


2. 

Chicago^  IIL,       July  20,      19 

Messrs.   A.  M.   THOMPSON  &  CO. 

Rochester,   N.Y. 

Bought  of  Nelson,  Morris  &  Co* 

Terms  50  da 


tubs   Lard 
72-17     70-14 
69-14     71-14 
71-15     70-16 


*#* 


casks  Shoulders 
421-65  426-70 
424-72  422-64 
427-72  421-60   #**# 

casks  Hams 

409-72  412-70 
414-71  410-73 
412-70  416-71   *### 


$0.13 


14 


.18 


43 


299 


368 


29 


32 


28 


**# 


#* 


3.  The  gross  weights  and  tares  of  6  casks  of  shoulders  are 
as  follows  :  428  -  68,  419  -  70,  423  -  63,  432  -  72,  436  -  69, 
484  -  65  lb.     Find  the  total  net  weight. 

4.  The  gross  weight  and  tares  of  12  tubs  of  lard  are  as  fol- 
lows :  71-14,  70-15,  69-14,  71-15,  72-17,  73-17, 
69-15,  71-16,  72-15,  73-16,  74-17,  75-17  lb.  Find 
the  total  net  weight. 

5.  The  gross  weights  and  tares  of  10  bbl.  of  sugar  are  as 
follows:  319-18,  331-19,  329-17,  334-20,  338-21, 
325  -  18,  326  -  16,  325  -  19,  327  -  19,  321  -  17  lb.  Find  the 
total  net  weight. 


SUBTRACTION 


33 


WRITTEN  EXERCISE 


Co'py  each  of  the  following  examples;  complete  the  work,  and 
check  the  result.  Time,  approximately,  thirty  minutes.  Face  of 
paper,  minus  discount  and  collection  and  exchange,  equals  proceeds. 


Face  of  Paper 

Discount 

Coll.  and  Exch. 

Proceeds 

1.   $376.25 

$3.76 

$0.38 

? 

255.78 

1.28 

0.26 

? 

176.44 

1.76 

? 

259.86 

2.60 

0.26 

? 

492.71 

2.46 

0.49 

? 

149.52 

0.75 

0.15 

? 

643.15 

6.43 

0.64 

? 

319.21 

0.80 
? 

? 

? 

? 

? 

Face  of  Paper 

Discount 

Coll.  and  Exch. 

Proceeds 

2.   $186.73 

$1.87 

$0.19 

? 

237.50 

2.38 

0.24 

? 

412.88 

4.13 

? 

337.95 

3.38 

0.34 

? 

360.90 

.    0.90 

? 

245.91 

1.23 

0.25 

? 

307.55 

3.08 

0.31 

? 

250.40 

3.76 

0.25 

? 

? 

? 

? 

? 

Face  of  Paper 

Discount 

Coll.  and  Exch. 

Proceeds 

3.    $421.95 

$2.11 

$0.42 

? 

112.70 

1.13 

0.11 

? 

324.50 

1.62 

? 

245.60 

2.46 

0.25 

? 

194.75 

0.92 

0.19 

? 

217.50 

1.09 

0.22 

? 

311.59 

3.12 

0.31 

? 

289.72 

1.45 

0.29 

? 

? 

? 

? 

? 

34 


CONCISE   BUSINESS   ARITHMETIC 


WRITTEN    EXERCISE 


Copy  each  of  the  following  examples  ;  find  the  new  balance^  the  total 
old  balance,  the  total  checks,  the  total  deposits,  and  check  the  work  : 


1. 

Name     Bal.   Checks  Deposits  Bal. 


Name     Bal.  Checks  Deposits  Bal. 


A 

$516 

$423 

$313 

? 

A 

$309 

$423 

$267 

? 

B 

203 

507 

398 

? 

B 

476 

379 

112 

? 

C 

195 

461 

412 

? 

C 

277 

407 

321 

? 

D 

204 

165 

? 

D 

255 

126 

? 

E 

335 

515 

296 

? 

E 

167 

217 

178 

? 

F 

411 

309 

156 

? 

F 

213 

453 

329 

? 

G 

135 

257 

145 

? 

G 

208 

196 

114 

? 

H 

295 

512 

? 

H 

126 

240 

114 

? 

I 

500 

316 

104 

? 

I 

255 

153 

? 

J 

450 

225 

117 

? 

J 

212 

317 

? 

K 

650 

751 

211 

? 

K 

455 

235 

103 

? 

L 

512 

337 

206 

? 

L 

275 

230 

115 

? 

M 

242 

176 

105 

? 

M 

315 

275 

144 

? 

? 

? 
3. 

? 

? 

? 

? 

4. 

? 

? 

Name 

;  Bal. 

Checks  Deposits  Bal. 

Name 

:  Bal. 

Checks  Deposits 

Bai 

A 

$311 

$242 

$301 

? 

A 

$267 

$133 

$145 

? 

B 

235 

115 

118 

? 

B 

247 

315 

? 

C 

178 

212 

? 

C 

256 

119 

228 

? 

D 

142 

188 

206 

? 

D 

116 



177 

? 

E 

268 

315 

? 

E 

215 

411 

196 

? 

F 

447 

397 

109 

? 

F 

423 

375 

116 

? 

G 

214 

375 

226 

? 

G 

198 

213 

132 

? 

H 

154 

106 

? 

H 

245 

157 

109 

? 

I 

256 

400 

144 

? 

I 

233 

334 

168 

? 

J 

512 

613 

199 

? 

J 

443 

337 

155 

? 

K 

245 

237 

155 

? 

K 

704 

856 

266 

? 

L 

146 

114 

? 

L 

231 

250 

119 

? 

M 

565 

743 

248 

? 

M 

178 

252 

107 

? 

? 

? 

? 

? 

? 

? 

? 

? 

SUBTRACTION  35 

A  WRITTEN   REVIEW  TEST 

Write  problems  1  and  2  from  dictation^  and  then  complete  the 
work,    Time^  approximately^  forty  minutes^  including  the  dictation. 

1.    Add  the  following  and  check  the  results : 

3412  4571 

6243  8132 

1729  2642 

4572  7235 

2643  6254 

3414  8149 

7145  6127 

3328  2170 

5331  4262 

3473  1208 


2.    Find  the  new  balance,  the  total  old  balance,  the  total 
checks,  the  total  deposits,  and  check  the  work : 


3582 

? 

2738 

? 

9810 

? 

1345 

? 

4165 

? 

3542 

? 

4713 

? 

2312 

? 

1745 

? 

8052 

? 

? 

? 

AME 

Balance 

Checks 

Deposits 

Bala 

A 

$235 

$142 

$217 

? 

B 

312 

254 

122 

? 

G 

288 

•300 

212 

? 

D 

542 

250 

106 

? 

E 

350 

500 

? 

F 

600 

325 

? 

G 

750 

252 

? 

H 

219 

200 

151 

? 

I 

224 

100 

216 

? 

J 

116 

330 

214 

? 

K 

255 

225 

110 

.    ? 

? 

? 

? 

? 

? 

3.  The  text,  page  14,  problem  4. 

4.  The  text,  page  14,  problem  5. 

5.  The  text,  page  14,  problem  6. 


CHAPTER  IV 

MULTIPLICATION 
ORAL  EXERCISE 

1.  Which  of  the  following  numbers  are  concrete  ;  that  is,  re- 
fer to  some  particular  kind  of  object  or  measure?  12  ;  5|-;  12 
ft.  ;  2.5  da.  ;  15  yd.  ;   18  men  ;   200;  $12  ;   172f 

2.  Which  of  the  above  numbers  are  abstract ;  that  is,  do  not 
refer  to  any  particular  kind  of  object  or  measure  ? 

3.  5  +  4  +  2-1-8  +  9  =  ? 

4.  9  +  9  +  9  +  9  +  9=?   5  times  9  =  ? 

5.  Could  the  sum  of  the  numbers  in  problem  3  be  found  by 
any  shorter  process? 

6.  What  is  the  first  process  in  problem  4  called  ?   the  second? 

7.  9  times  27  =  ?     9  times  29  bu.  =  ? 

8.  If  1  bu.  of  rye  weighs  56  lb.,  what  will  12  bu.  weigh? 

46.  In  problems  7  and  8  it  is  seen  that  the  multiplier  is 
always  an  abstract  number  ;  and  tlie  multiplicand  and  product  are 
like  numbers. 

47.  Three  5's  are  equal  to  five  3's  ;  $3  multiplied  by  5  is 
equal  to  $5  multiplied  by  3  ;  4  trees  multiplied  by  125  is  equal 
to  125  trees  multiplied  by  4. 

48.  It  is  therefore  seen  that  the  product  is  not  affected  by 
changing  the  order  of  the  factors  regarded  as  abstract  numbers. 

49.  The  multiplicand  and  multiplier  together  are  called 
factors  (makers)  of  the  product  ;  the  product  of  two  abstract 
integers  is  sometimes  called  a  multiple  of  either  of  the  factors. 

50.  Sometimes  a  number  is  used  several  times  as  a  factor. 
Numbers  so  used  are  indicated  by  a  small  figure,  called  an  expo- 
nent, written  above  and  at  the  right  of  the  factor. 

Thus,  4  used  twice  as  a  factor  is  written  4^,  5  used  four  times  as  a  factor 
is  written  5*,  and  6  used^ye  times  as  a  factor  is  written  6^. 


MULTIPLICATION  37 

51.  The  product  arising  from  using  a  number  two  or  more 
times  as  a  factor  is  called  a  power  of  that  number. 

Thus,  4  is  the  second  power  of  2  ;  64  is  the  third  power  of  4  and  the  sixth 
power  of  2. 

Too  much  attention  should  not  be  given  to  the  definitions  like  the  above. 
They  are  valuable  only  as  they  help  to  make  clear  the  matter  in  the  exercises. 
They  are  rarely  heard  in  business  and  therefore  should  not  be  memorized. 

ORAL  EXERCISE 

1.  Multiply  at  sight  each  number  below  by  2 ;  by  3 ;  by  4  ; 
by  5;  by  6;  by  7;  by  8 ;  by  9. 

Name  the  products  by  lines  from  left  to  right  and  from  right  to  left; 
also  by  columns  from  left  to  right  and  from  right  to  left.  Name  results 
only.  Thus,  to  multiply  lines  by  4  say  20,  36,  8,  24,  40,  12,  28,  44,  16,  48, 
32,  52,  68, 84,  and  so  on  up  to  100 ;  and  backwards,  100,  80,  96,  64,  and  so  on 
back  to  20.  To  multiply  columns  by  4  say  20,  68,  36,  84,  and  so  on  to  52, 
100 ;  and  backwards  100,  52,  80,  32,  and  so  on  to  68,  20.  Continue  the  work 
until  results  can  be  named  at  the  rate  of  120  or  more  per  minute. 

5        9      2      6      10      8      7      11      4      12      8      13 
17      21    14    18      22    15    19      23     16      24     20      25 

2.  Multiply  as  instructed  in  problem  1  and  add  8  (carried) 
to  each  product.  Also  multiply  as  instructed  and  add  6,  4,  7, 
2,  5,  3,  and  9  to  each  product. 

Name  results  only.  Thus,  to  multiply  by  lines  say  20,28;  36,  44;  8, 
16  ;  and  so  on. 

3.  Multiply  by  2  :  27,  35,  81,  36,  28,  32,  47,  93,  56,  39,  54, 
45,  52,  86,  75,  67,  59.     Also  by  4,  3,  5,  8,  6,  7,  9. 

4.  Find  the  cost  of  each  of  the  following:  20  lb.  crackers  at 
8^;  9  lb.  coffee  at  34^;  7  lb.  tea  at  57^;  11  lb.  beef  at  17^; 
120  lb.  sugar  at  4^;  134  lb.  sugar  at  5^. 

5.  Find  the  cost  of  each  of  the  following:  44  yd.  at  9^;  37 
yd.  at  8^;  123  yd.  at  6^;  214  yd.  at  4^;  52  yd.  at  12^;  29 
yd.  at  8^;  8  yd.  at  $1.08;   7  yd.  at  f  1.01;  5  yd.  at  11.35. 

6.  Beginning  at  0  count  by  9's  to  81 ;  by  lO's  to  150 ;  by  ll's 
to  154;  by  12's  to  108;  by  13's  to  117;  by  14's  to  126;  by 
15's  to  135 ;  by  16's  to  144 ;  by  17's  to  153 ;  by  18's  to  162 ;  by 
19's  to  171 ;  by  20's  to  180. 


38  CONCISE   BUSINESS   ARITHMETIC 

52.   Examples,    i.  Find  the  cost  of  2150  lb.  at  5^. 

Solution.     Since  1  lb.  costs  5^,  2150  lb.  will  cost  2150  times      ^  21.50 
6f;  but  2150  times  5^    is  equal  to  5  times   2150)2^.    5    times  5 

$21.50  (2150 )>)  equals  $107.50,  the  required  result.  ^  107.50 

2.  Multiply  224  by  46. 

Solution.    In  multiplying  one  number  by  another,  224  224 

there  is  no  practical  advantage  in  beginning  with  the  45  4.Q 

lowest  order  of  units  of  the  multiplier ;   in  fact,  in  "TqTZ  00^ 

some  multiplications  there  is  a  decided  advantage  ^q^  ^  n^, 

in  beginning  with  the  highest  order.    The  arrange-  . 

ment  of  work  for  both  methods  is  shown  in  the  10oU4        lUoUi 

margin. 

Check.  The  work  may  be  checked  by  multiplying  first  by  one  method  and 
then  by  the  other,  or  by  interchanging  the  multiplier  and  multiplicand  and  re- 
multiplying.     (See  also  pages  73  and  74.) 

3.  Multiply  2004  by  1275. 

Solution.     When  one  of  two  numbers  to  be  mul-              1275  1275 

tiplied  contains  a  number  of  zeros  or  ones,  it  is  always             2004  2004 

easier  to  take  that  number  as  the  multiplier.     Since  ^M)0  9c c a 

the  product  of  any  number  multiplied  by  0  is  0,  the  occa  ^      ^1  Ort 

product  of  1275  multiplied  by  the  tens  and  hundreds  — '- 

of  the  multiplier  need  not  be  written.  2555100  2555100 

Check.    The  problem  may  be  checked  the  same  as  problem  2. 

When  two  numbers  are  to  be  multiplied,  it  is  generally  easier  to  take  as 
the  multiplier  the  number  having  the  least  number  of  places.  Thus,  to  find 
the  cost  of  1647  A.  of  land  at  $27  per  acre,  take  27  as  the  multiplier. 

If  one  of  the  two  numbers  to  be  multiplied  has  two  or  more  digits  alike, 
it  is  easier  to  take  that  number  as  the  multiplier.  Thus,  to  multiply  to- 
gether 6729  and  7777,  it  is  easier  to  take  7777  as  the  multiplier. 

ORAL   EXERCISE 

1.  Find  the  value  of  51  T.  of  hay  at  $11  per  ton. 

2.  Find  the  cost  of  175  lb.  of  sugar  at  5^  per  pound. 

3.  How  much  will  a  boy  earn  in  87  hr.  at  9^  an  hour? 

4.  What  is  the  cost  of  a  flock  of  52  sheep  at  $7  per  head? 

5.  At  the  rate  of  47  mi.  an  hour,  how  far  will  a  person 
travel  in  12  hr.  ? 

6.  What  is  the  cost  of  12  pr.  of  shoes  at  f  4.50  per  pair,  and 
8  pr.  of  boots  at  $3.50  per  pair? 


MULTIPLICATION  39 

7.  What  must  be  paid  for  handling  12  loads  of  freight  at 
$2.25  per  load? 

8.  In  an  orchard  there  are  13  rows  of  trees,  each  containing 
21  trees.     How  many  trees  in  the  orchard? 

9.  If  you  buy  5  pencils  at  9^  each  and  9  penholders  at  5^ 
each,  and  some  stationery  costing  25^,  how  much  change  should 
you  receive  from  a  two-dollar  bill?  from  a  ten-dollar  bill? 

10.  I  bought  6  cd.  of  wood  at  $5.75  per  cord.  If  a  fifty- 
dollar  bill  is  offered  in  payment,  how  much  change  should  be 
received  ? 

11.  I  bought  12  bu.  of  wheat  at  $1.05.  If  I  gave  in  pay- 
ment two  ten-dollar  bills,  what  change  should  I  receive? 

12.  My  average  marketing  expenses  per  day  are  $2.10.  If  I 
offer  a  twenty-dollar  bill  in  payment  for  7  days'  expenses,  what 
change  should  I  receive? 

13.  I  sold  16  chairs  at  $7  each,  and  5  tables  at  $9  each.  If 
two  one-hundred-dollar  bills  are  offered  in  payment,  how  much 
change  should  I  return?  If  a  one-hundred-dollar  bill,  a  fifty- 
dollar  bill,  and*  a  twenty-dollar  bill  are  offered  in  payment,  how 
much  change  should  I  return? 

WRITTEN  EXERCISE 

In  the  following  problems  find  the  missing  numbers  by  multiply- 
ing across  and  adding  down.  Qheek  the  results  by  comparing  the 
sum  of  the  line  products  with  the  sum  of  the  multiplicands  multi- 
plied by  one  of  the  multipliers. 

1.  2.  3. 

15x211=?  9x1475=?  12  x  $16.50=? 

15x346=?  9x2618=?  12  x  $27.75=? 

15x318=?  9x1575=?  12  x  $14.95=? 

15  X  721  =  ?  9  X  1792  =  ?  12  x  $29.86=  ? 

15x936=?  9x4936=?  12  x  $49.88=? 

15x849=?  9x7289=?  12  x  $39.62=  ? 

15x218=  ?  9x8728=_?,  12  x  $86.99=  ? 

15  X    ?    =  ?  9  x     ?    =  ?  12  X      ?      =  ? 


40  CONCISE   BUSINESS   ARITHMETIC 

4.  5.  6. 

12x192=?  98x2178=?  16  xf  18.10=? 

12x721=?  98x1692=?  16  x    17.20=? 

12  X  836  =  ?  98  X  2536  =  ?  16  x    21.40  =  ? 

12x456=?^  98x2892=  ?  16  x    25.85=  ? 

12  X    ?    =  ?  98  X     ?     =  ?  16  X       ?      =  ? 

Problems  such  as  the  above  are  very  helpful.  They  aiford  a  variety  of 
work  and  suggest  a  simple  method  by  which  the  student  may  test  the  cor- 
rectness of  his  results.  The  instructor  should  add  as  many  more  problems 
as  circumstances  require. 

7.  A  produce  dealer  bought  2145  bu.  of  potatoes  at  83/  a 
bushel,  and  sold  them  at  S1.05  a  bushel.     What  did  he  gain  ? 

8.  A  drover  bought  125  head  of  cattle  at  $15.75  per  head. 
He  sold  65  head  at  $23.40,  15  head  at  $13.75,  and  45  head  at 
$17.75.    Did  he  gain  or  lose,  and  how  much? 

9.  A  grocer  bought  14  bu.  of  apples  at  $1.35  per  bushel  and 
12  bu.  of  potatoes  at  84/  per  bushel.  He  sold  the  apples  at  40/ 
a  peck  and  the  potatoes  at  25/  a  peck.    What  did  he  gain  ? 

10.  A  bought  1247  bbl.  of  apples  at  $3.10  per  barrel.  After 
holding  them  for  three  months  he  sold  them  at  $4.80  per  barrel. 
If  he  paid  $74.82  for  storage,  and  his  loss  by  decay  was  37  bbl. 
of  apples,  what  was  his  gain  ? 

11.  The  gross  weight  in  pounds,  and  tare  in  pounds,  of  25 
tubs  of  lard  are  as  follows  :  71  -  14,  70  -  15,  69  -  14,  72  - 16, 
71-14,  72-15,  70-15,  69-14,  71-15,  70-15,  69-14, 
71-16,  71-15,  71-14,  70-15,  68-14,  73-16,  73-15, 
70-14,  70-14,  71-15,  73-16,  74-18,  71-13,  73-16. 
Find  the  cost  at  13^  per  pound. 

12.  The  gross  weight  in  pounds,  and  the  tare  in  pounds,  of 
25  casks  of  hams  are  as  follows :  400  -  78,  420  -  68,  420  -  71, 
403-71,  409-71,  418-68,  412-72  407-67,  423-69, 
419-67,  426-68,  403-70,  399-69,  400-69,  425-71, 
413-72,  399-67,  412-72,  418-68,  409-71,  408-70, 
412-68,  402-71,  421-71,  403-71.  Find  the  cost  at 
18^   per  pound. 


MULTIPLICATION  41 

SHORT   METHODS    IK   MULTIPLICATION 

53.  There  are  many  short  methods  in  multiplication,  but  of 
these  only  a  few  are  practical,  either  because  they  apply  generally 
to  problems  that  in  themselves  are  not  practical  or  because  they 
have  been  supplanted  by  the  elaborate  use  of  tables  and  mechani- 
cal devices.  A  great  many  practical  and  helpful  tables  are  in 
use  for  figuring  pay  rolls,  interest,  discount,  and  the  like.  These 
tables  are  great  time  savers. 

54.  The  machines  that  are  used  for  adding,  subtracting,  multi- 
plying, dividing,  and  for  setting  forth  results  in  interest  and  dis- 
count are  now  in  such  common  use  that  a  chapter  is  devoted  to 
then*  consideration  in  Appendix  A  at  the  close  of  this  volume. 
These  machines  are  found  in  business  offices,  especially  where 
extensive  operations  are  to  be  performed.  Both  in  accuracy  and 
in  the  saving  of  time  they  are  most  valuable. 

55.  The  short  methods  given  herewith  have  a  wide  applica- 
tion. They  are  not  dependent  upon  formal  rules,  and  are  sug- 
gestive of  other  ways  in  which  the  student  may  exercise  his  own 
ingenuity  to  shorten  his  work  in  multiplication. 

Multiplication  by  Powers  and  Multiples  of  Ten 
oral  exercise 

1.  40  is  how  many  times  4  ?  60  is  how  many  times  6  ?  100 
is  how  many  times  10?     150  is  how  many  times  15? 

2.  Give  a  short  method  for  multiplying  an  integer  by  10. 

3.  400  is  how  many  times  4?  600  is  how  many  times  6? 
1000  is  how  many  times  10?     1500  is  how  many  times  15? 

4.  Give  a  short  method  for  multiplying  an  integer  by  100; 
by  1000  ;  by  10000. 

5.  How  does  the  product  of  40  x  66  compare  with  the 
product  of  4  X  66  X  10  ?  the  product  of  400  x  59  with  the  prod- 
uct of  4x59  X  100? 

6.  Give  a  short  method  for  multiplying  an  integer  by  any 
number  of  lO's,  lOO's,  or  lOOO's. 


42  COKCISE   BUSINESS   ARITHMETIC 

7.  Multiply  270  by  300. 

Solution.     In  the  accompanying  illustration  "70       =27  X  10 

it  will  be  seen  that  270  x  300  =  27  x  3  x  1000  300    =     3  X  100 

^'^  ^^'^^^-  81000  =  81 X  1000 

8.  Formulate  a  rule  for  finding  the  product  when  there  are 
zeros  on  the  right  of  both  factors. 

9.  $7  is  how  many  times  $0.70?    $90  is  how  many  times 
$0.90?   $500  is  how  many  times  $0.50? 

10.  State  a  short  method  for  multiplying  United  States 
money  by  10 ;  by  100 ;  by  1000. 

11.  Read  aloud  the  following,  supplying  the  missing  words : 
(a)    Annexing  a  cipher  to  an  integer  multiplies  the  integer 

by ;  annexing  two  ciphers  to  an  integer the  integer 

by . 

(5)    Removing  the   decimal  point   in  United  States  money 

one  place  to  the  right the  number  by  10 ;  removing  the 

decimal  point  two  places  to  the  right the  number  by . 

12.  Multiply  $14.70  by  10 ;  by  100 ;  by  1000. 

56.    In  the  above  exercise  it  is  clear  that 

Annexing  a  cipher  to  an  integer  multiplies  the  integer  hy  10; 
and 

Removing  the  decimal  point  one  place  to  the  right  multiplies 
the  number  hy  10. 

ORAL  EXERCISE 

1.  Read  aloud  the  following  numbers  multiplied  by  10 ;  by 
100;  by  1000:     17;  285;  3712;  $413.45 ;  $1926.75 ;  4165.95. 

2.  Read  each  of  the  following  numbers  multiplied  by  20;  by 
400;  by  600;  by  5000:       16 ;  19  ;  37 ;  49^;  64^;  $122;  $2.60. 

3.  By  inspection  find  the  cost  of : 

650  yd.  silk  at  $1.20. 
140  bu.  beans  at  $3.50. 
500  bu.  beans  at  $2.50. 
240  gro.  jet  buttons  at  $3. 
500  doz.  half  hose  at  $5.50. 
800  yd.  taffeta  silk  at  $1.20. 


a. 

750  lb.  coffee  at  30)^. 

fl- 

h. 

500  lb.  cocoa  at  40^. 

h. 

c. 

650  lb.  chocolate  at  50^. 

i. 

d. 

300  bbl.  lump  salt  at  $3. 

J- 

e. 

200  bbl.  oatmeal  at  $4.50. 

k. 

/. 

170  bx.  wool  soap  at  $3. 

I 

MULTIPLICATION  43 

57.  When  the  multiplier  is  a  number  a  little  less  than  10, 
100,  or  1000,  the  multiplication  may  be  shortened  as  shown 
in  the  following  examples. 

58.  Examples,     l.    Multiply  123  by  99. 

Solution.    9D  is  100  diminished  by  1;  hence,  multiply  123 
by  100  and  then  by  1  and  subtract  the  results.    The  product  is  123 

12,177.     Check  by  retracing  the  steps  in  the  process.  12177 

2.    Multiply  145  by  96. 

Solution.     96  is  100    diminished  by  4 ;  hence,  multiply  145 
by  100  and  then  by  4  ctnd  subtract  the  results.    The  product  is  580 

13,920.    Check  by  retracing  the  steps  in  the  process.  13920 


12300 


14500 


WRITTEN  EXERCISE 

1.    Find  the  total  cost  of  : 

5260  bu.  rye  at  99^.  834  bu.  millet  at  95^. 

1521  bu.  rye  at  92^.  246  bu.  wheat  at  92^. 

1640  bu.  wheat  at  98^.  998  bu.  millet  at  il.04. 

2994  bu.  millet  at  97^.  998  bbl.  apples  at  11.05. 

1112  bu.  wheat  at  97^.  893  bkt.  peaches  at  11.05. 

2160  bu.  millet  at  96^.  993  bu.  clover  seed  at  f  3.35. 

Multiplication  by  11  and  Multiples  op  11 
59.    Example.     Multiply  237  by  11. 

Solution.  To  multiply  by  11  is  to  multiply  by  10  +  1.  Hence,  annex  a 
cipher  to  237  and  add  237  ;  or,  better  still,  add  the  digits  as  follows  :  7  ;  3  +  7  = 
10 ;  3  +  2+1  (carried)  =  6  ;  bring  down  2  ;  therefore,  the  result  is  2607. 

ORAL  EXERCISE 

1.  Multiply  each  of  the  following  by  11: 

14;  26;  45;  19;  16;  34;  36;  49;  64;  125;  112;  115; 
128;  192;  175;  116;  142;  14.95;  $9.62;  14.41;  $6.82; 
$5.21;  $3.65;  $4.31;  $21.12;  $14.21;  $18.32;  $3.26. 

2.  Find  the  cost  of  11  yd.  at  27^;  at  91^;  at  86^;  at 
95^;  at  $1.49;  at  $1.23;  at  $2.17;  at  $2.31;  at  $2.40;  at 
$2.50;  at  $2.75;  at  $4.35;  at  $3.15;  at  $3.10;  at  $8.13. 


44  CONCISE  BUSINESS  ARITHMETIC 

60.    Examples,     i.    Multiply  46  by  22. 

Solution.    22  is  11  times  2.     Multiply  46  by  11  and  by  2,  as  fol- 

lows  :  2x6  =  12;  write  2  and  carry  1.    4  +  6  =  10 ;  2  x  10  +  1  (car-  "*" 

ried)  =  21  ;  write  1  and  carry  2.   2x4  +  2  (carried)  =  10  ;  write  10.  22 

The  result  is  1012.  1012 

2.    Find  the  cost  of  122  bu.  of  potatoes  at  66  j^  per  bu. 

Solution.     6x2  =  12;    write  2  and  carry   1.     2  +  2  =  4;6x4  -iqq 
+  1  (carried)  =  25  ;   write  5  and  carry  2.      l+2=3;6x3  +  2 

(carried)  =  20  ;  write  Oand carry  2.    0x1+2  (carried)  =  8.    Write  -^^ 

8.    The  result  is  $80.52.  80.52 


WRITTEN   EXERCISE 

In  the  following  problems  make  all  the  extensions  mentally, 

1.  Find  the  total  cost  of  : 

11  lb.  coffee  at  42^.  115  bu.  rye  at  99^. 

14  doz.  eggs  at  21^.  215  bu.  peas  at  77^. 

64  lb.  cheese  at  22^.  344  bu.  oats  at  44^. 

33  bu.  carrots  at  56^.  300  bu.  grain  at  85^. 

11  bu.  potatoes  at  85^.  115  bu.  barley  at  88^. 

88  bu.  wheat  at  88/.  400  bbl.  apples  at  {|3.25. 

2.  Find  the  total  cost  of  : 

77  bu.  peaches  at  $1.85.  820  bu.  rye  at  88^. 

151  bu.  corn  at  66^,  327  bu.  oats  at  33^. 

265  bu.  onions  at  80^.  314  bu.  peas  at  66^. 

135  bu.  apples  at  82^.  110  bu.  pears  at  $1.66. 

241  bu.  turnips  at  44^.  880  bu.  barley  at  $  1.17. 

112  bu.  tomatoes  at  55^.  100  bu.  quinces  at  11.60. 

A  careful  computer  checks  his  work  at  every  step.  The  student  who 
forms  the  habit  of  doing  this  in  all  his  computations  will  soon  find  himself 
in  no  need  of  printed  answers  to  problems  involving  only  numerical  calcula- 
tion. 

Checks  for  multiplication  have  already  been  mentioned.  To  guard 
against  large  errors,  it  is  also  important  to  form  a  rough  estimate  of  an 
answer  before  beginning  the  solution.  Thus,  in  finding  the  cost  of  211  yd. 
of  lining  at  32j^,  at  once  see  that  the  result  will  be  a  little  more  than  ^63.00 
(210  times  30^);  this  will  do  away  with  such  absurd  results  as  $6752, 
$675.20,  or  $6.75. 


MULTIPLICATION 
3.    Copy  and  find  the  amount  of  the  following  bill: 

Boston,  Mass.,         July   21,  19 

Mrs.  GEORGE  W.  MUNSON 

168  Huntington  Ave.,  City 

Bought  of  S.  S.  PIERCE  COMPANY 

Tenns  Cash 


45 


15 
25 
31 
55 
212 

cs.  Horse-radish 
lb.  Huyler*s  Cocoa 
gal.  N.  0.  Molasses 
lb.  Japan  Tea 
u  Raisins 

$0.66 
.44 
.63 
.48 
.11 

MULTIPLICATIOlSr   BY    25,    50,   AND    75 

61.  Annexing  two  ciphers  to  an  integer  multiplies  it  by  100. 
Removing  the  decimal  point  two  jjlaces  to  the  right  multiplies 
the  decimal  by  100. 

62.  Example.     Multiply  76  by  100. 

Solution.  76  x  100  =  7600.  (Annexing  the  two  ciphers  gives  the  required 
result  without  the  necessity  for  a  written  solution.) 

63.  Example.     Multiply  148  by  25. 

Solution.     148  x  100  =  14,800.     14,800  --  4  =  3700. 

Hence,  to  multiply  an  integer  by  25,  annex  two  ciphers  to  the  multiplicand 
and  then  divide  by  4. 

64.  Example.     Multiply  278  by  50. 

Solution.     278  x  100  =  27,800.     27,800  -  2  =  13,900. 

Hence,  to  multiply  an  integer  by  50,  annex  two  ciphers  to  the  multiplicand 
and  then  divide  by  2. 

65.  Example.     Multiply  48  by  75. 

Solution.     48  x  100  =  4800.     4800  ^  4  =  1200 ;  3  x  1200  =  3600. 
Hence,  to  multiply  an  integer  by  75,  annex  two  ciphers  to  the  multiplicand, 
divide  that  product  by  4,  and  then  multiply  by  3. 


46 


CONCISE   BUSINESS   AEITHMETIC 


ORAL  EXERCISE 

State  the  product  of: 

• 

1.    36  X  25. 

8. 

48  X  50. 

15. 

64  X  75. 

2.   27x50. 

9. 

52  X  75. 

16. 

63  X  25. 

3.   28x75. 

10. 

67  X  50. 

17. 

69  X  25. 

4.   97x25. 

11. 

89  X  50. 

18. 

56  X  75. 

5.    248  X  25. 

12. 

186  X  50. 

19. 

240  X  75, 

6.   126x50. 

13. 

146  X  25. 

20. 

184  X  75. 

7.   164x25. 

14. 

204  X  50. 

21. 

144  X  75. 

WRITTEN   EXERCISE 


In  the  following  problems  make  all  the  extensions  mentally, 
1.    Find  the  total  cost  of : 


42  lb.  cocoa  at  40  /. 
45  lb.  cocoa  at  50/. 
50  lb.  cofPee  at  28/. 
25  lb.  raisins  at  15/. 
23  lb.  tea  at  40/. 

2.    Find  the  total  cost  of : 
36  yd.  wash  silk  at  25/. 
25  doz.  whalebones  at  92/. 
97  yd.  cloth  at  75/. 
25  gro.  buttons  at  35/. 
29  yd.  gunner's  duck  at  19/. 


27  bx.  salt  at  50/. 
23  lb.  coffee  at  25/. 
21  lb.  candy  at  75/. 
33  lb.  chocolate  at  50/. 
85  lb.  Oolong  tea  at  45/. 

87  yd.  flannel  at  50/. 
21  yd.  cottonade  at  18/. 
25  yd.  denim  at  19/. 
17  yd.  dress  goods  at  50/ 
23  yd.  cheviot  at  21/. 


Multiplication  by  an  Even  Number  of  Hundreds 

66.  Example.     Multiply  468  by  300. 

Solution.     468  x  100  =  46,800  ;  46,800  x  3  =  140,400. 

Hence,  to  multiply  an  integer  by  an  even  number  of  hundreds,  annex  two 
ciphers  to  the  multiplicand  and  then  multiply  by  the  significant  figure  in  the 
multiplier. 

67.  The  value  of  many  short  methods  is  that  they  enable 
one  to  write  results  quickly  without  performing  the  mechanical 
operations. 


MULTIPLICATION  47 

68.  Many  short  methods  in  multiphcation  are  not  practical 
because  they  require  one  to  remember  so  many  things,  or  they 
apply  to  so  few  numbers  that  it  is  impossible  for  an  ordinary 
person  to  remember  them.  The  short  methods  given  in  this 
text  are  practical. 

ORAL  EXERCISE 

Find  the  product  of: 

1.  234  X  200.  7.  753  x  300.  13.  964  x  200. 

2.  175  X  600.  8.  845  x  400.  14.  554  x  300. 

3.  335  X  800.  9.  453  x  200.  15.  181  x  700. 

4.  216  X  900.  10.  256  x  400.  16.  312  x  800. 

5.  648x100.  ^          11.  145x800.  17.  237x600. 

6.  452  X  500.  12.  333  x  700.  18.  122  x  900. 

Multiplication  by  Numbers  from  101  to  109  Inclusive 

69.  Examples,     l.  Find  the  cost  of  64  bu.  of  wheat  at  i  1.02. 

Solution.    2  x  64  =  128  ;  write  28  and  carry  1.     1  x  64  +1  =  "* 

65 ;  write  65.      The  result  is  ^  65.28.  1.02 

Some  persons  may  prefer  to  work  this  problem  as  follows  :  64  65.28 
bu.  at$l=f64;  64  bu.  at  2^  =  11.28;  $64  +  $1.28  =  $65.28. 

2.   Find  tlie  cost  of  251  bu.  of  barley  at  $1.04. 

Solution.    4  x  51  =  204  ;   write  04  in  the  product  and  cany  2.  251 

4x2  +  2  (carried)  +  1  (the  right-hand  figure  of  the  multiplicand)  -i  qa 

=  11  ;  write  1  and  carry  1.     1  x  25  +  1  (carried)  =  26 ;  write  26. 
The  result  is  $261.04. 


261.04 


70.  Similarly  multiply  by  such  numbers  as  201,  302,  and  405. 

71.  Example.     Find  the  cost  of  124  bu.  of  beans  at  I  2.05. 

Solution.    5  x  24  =  120.     Write  20  and  carry   1.      5x1+1  124 

(carried)  +2x4  (the  right-hand  figure  of  the  multiplicand)  =  14 ;  9  O'^ 

write  4  and  carry  1.     2  x  12  +  1  (carried)  =  25  ;  write  25.     The  ' 

result  is  $  254.20.  254.20 

Some  persons  may  prefer  the  following  solution  :  124  bu.  at  $2  =  $248; 

124  bu.  at  5^  =  $6.20;  $ 248 +  $ 6.20  =  $ 254.20.     The  student  should  try 
to  exercise  his  own  ingenuity  in  all  this  work. 


48 


CONCISE   BUSINESS   ARITHMETIC 


WRITTEN  EXERCISE 


Find  the  value  of: 

1.  215  T.  coal  at  $6.05. 

2.  224  bu.  rye  at  11.02. 

3.  215  bu.  wheat  at  $1.02. 

4.  318  bu.  barley  at  f  1.05. 

5.  124  bbl.  apples  at  12.05. 

6.  116  bbl.  onions  at  11.08. 


8.  302  bu.  peas  at  74  ^, 

9.  104  bu.  corn  at  89  ^. 

10.  103  bu.  beets  at  85  ^. 

11.  205  bu.  turnips  at  54  ^. 

12.  215  bu.  pears  at  $1.05. 

13.  411  bu.  plums  at  $1.08. 


7.    232  bbl.  potatoes  at  $2.05.     14.   206  bu.  parsnips  at  93^. 

Miscellaneous  Short  Methods 

72.  When  one  part  of  the  multiplier  is  contained  in  another 
part  a  whole  number  of  times,  the  multiplication  may  be  short- 
ened as  shown  in  the  following  examples. 

73.  Example.     Multiply  412  by  357. 

Solution.  35  is  5  times  7.  7  X  412  =  2884,  which 
write  as  the  first  partial  product.  5  x  2884  =  14,420, 
which  write  as  the  second  partial  product. 

Check.  Interchange  the  multiplier  and  multipli- 
cand and  remultiply.  4  x  357  =  1428  ;  3  x  1428 =4284. 
Add.  Since  the  results  by  both  multiplications  agree, 
the  work  is  probably  correct. 


412 
357 


2884 

14420    

147084   147084 


357 
412 
1428 
4284 


74.   Example.     Multiply  214  by  756. 

Solution.  56  is  8  times  7.  7  x  214  =  1498,  which  we  write  as 
the  first  partial  product.  8  x  1498  =  11,984,  which  we  write  as  the 
second  partial  product.  The  sum  (161,784)  of  these  partial  products 
is  the  entire  product. 

Check  as  in  problem  1.     (See  also  pages  73  and  74.) 


214 

756 


1498 

11984 
161784 


WRITTEN   EXERCISE 

Find  the  product  of: 

1.  319  X  248.  3.    728  x  287. 

2.  927  X  279.  4.   848  x  369. 

The  above  short  methods  are  practical  in  a  limited  num- 
ber of  problems. 


MULTIPLICATION 


49 


WRITTEN  REVIEW  EXERCISE 


1.   Use  6  as  a  multiplier  for  each  column.     Check.     (See 
page  39.) 


a. 

h. 

c. 

d. 

e. 

m 

74 

39 

126 

215 

48 

63 

58 

232 

175 

73 

52 

82 

311 

243 

49 

65 

72 

135 

223 

45 

55 

85 

144 

183 

(6^ 

47 

19 

225 

253 

11 

88 

92 

245 

127 

2.  Use  8  as  a  multiplier  for  each  column.     Check. 

3.  I  bought  15  A.  of  land  at  $275  per  acre  and  laid  it  out  in 
100  city  lots.  After  expending  S6750  for  grading  and  taxes, 
$257  for  ornamental  trees,  and  $250  for  advertising,  I  sold 
15  lots  at  $625  each,  35  lots  at  $415  each,  and  exchanged  the 
remainder  for  a  farm  of  120  A.,  which  I  immediately  sold  at 
$195  per  acre.     Did  I  gain  or  lose,  and- how  much? 

4.  Copy  and  find  the  amount  of  the  following  bill : 


RocLester,  N.Y.,        July  26, 

Mr.   F.    C.    GORHAM 

120  Spring  Street,  City 

Bouglit  of  C.  E.  Ferguson  fe?  Son 
Terms    30    da. 


19 


37  bu. 

Oats 

JO.  40 

50   u 

Corn 

.67 

76   u 

Wheat 

1.02 

75   u 

Rye 

1.04 

95   u 

Beans 

4.00 

16   u 

Clover  Seed 

3.50 

26  a 

Millet 

.99 

50 


CONCISE   BUSINESS   ARITHMETIC 


WRITTEN   REVIEW 

Copy  these  examples ;  add  the  checks  in  the  Checks  in  Detail  columii 
and  enter  the  totals  in  the  Total  Checks  column ;  find  the  new  balance,  the 
total  old  balance,  the  total  checks,  the  total  deposits,  and  check  the  work. 


Checks  in 

Total 

Name 

Balancb 

Detail 

$180.55 

Checks 

Deposits 

Balance 

A 

$313.25 

211.15 
165.43 

208.19 

? 

$278.40 

? 

B 

285.67 

100.55 
145.97 

? 

327.44 

? 

C 

186.53 

200.12 

45.67 

118.95 

? 

198.45 

? 

D 

276.65 

205.18 

? 

210.50 

? 

E 

612  40 

? 

918.75 

? 

xu 

64.25 

F 

347.85 

103  86 

? 
? 

? 

X; 

6.84 
? 

? 

? 

? 

2. 

Checks  in 

Total 

Name 

Balance 

Detail 

Checks 

Deposits 

Balance 

A 

$195.63 

$214.70 

71.20 

8.50 

? 

$174.25 

? 

B 

98.40 

102.45 

74.65 

123.52 

? 

115.68 

? 

C 

153.30 

10.55 
75.20 
55.34 

? 

89.48 

? 

D 

386.54 

7.35 
172.38 
? 

? 
? 

275.40 

? 

? 

? 

? 

MULTIPLICATION  51 

A  WRITTEN  REVIEW  TEST 

Write  the  following  problems  from  dictation^  and  complete  the 
work.  Time,  approximately,  forty  minutes,  including  the  dictation. 
Mental  extensions  only, 

1.  Write  in  one  column,  and  find  the  total  value : 

78  yd.  at  11/  .               55  yd.  at  55/ 

69  yd.  at  25/  91  yd.  at  50/ 

60  yd.  at  85/  89  yd.  at  99/ 

45  yd.  at  98/  75  yd.  at  90/ 

37  yd.  at  97/  76  yd.  at  70/ 

112  yd.  at  99/  125  yd.  at  98/ 

2.  Write  in  one  column,  and  find  the  total  value : 

76  yd.  at  Sl.lO  82  yd.  at  S1.05 

55  yd.  at  $1.06  '             65  yd.  at  S1.20 

108  yd.  at  Sl.ll  130  yd.  at  $1.09 

b^  yd.  at  $1.25  83  yd.  at  $1.50 

88  yd.  at  $1.04  97  yd.  at  $1.03 

67  yd.  at  $1.02  137  yd.  at  $1.01 

3.  Write  in  one  column ;  use  11  as  the  multiplier,  and  check 
the  results : 

49,    16,    34,    78,    57,    73,    85,    94,    59,    64,    56,    81. 

4.  Write  in  one  column;  use  6  as  the  multiplier,  and  check 
the  results : 

125,  212,  350,  175,  162,  224,  319,  452,  133,  145,  121,  142. 

5.  Write  in  one  column ;  use  8  as  the  multiplier,  and  check 
the  results : 

45,    75,    62,    29,    76,    61,    19,    34,    85,    92,    27,    77. 

6.  Write  in  one  column ;  square  each  number,  and  total  the 
products : 

25,    55,    15,    45,    75,    35,  *  85,    65,    95. 

7.  The  text,  page  49,  problem  3,  in  the  Written  Review 
Exercise. 


CHAPTER  V 

DIVISION 
ORAL  EXERCISE 

1.  What  is  the  product  of  12  times  15?  How  many  times 
is  15  contained  in  180  ?     What  is  -^\  of  180  ? 

2.  How  much  is  11  times  $17?  How  many  times  is  $11 
contained  in  $187  ?     What  is  Jj  of  $187  ? 

3.  What  is  the  product  of  9  times  12  ft.?  How  many  times 
is  12  ft.  contained  in  216  ft.?     What  is  J^  of  225  ft.? 

4.  When  one  factor  and  the  product  are  given,  how  is  the 
other  factor  found  ? 

75.  The  process  of  finding  either  factor  when  the  product 
and  the  other  factor  are  given  is  called  division. 

76.  The  known  product  is  called  the  dividend;  the  known 
factor,  the  divisor;  the  unknown  factor,  when  found,  the 
quotient. 

77.  The  part  of  the  dividend  remaining  when  the  division 
is  not  exact  is  called  the  remainder. 

While  definitions  such  as  the  above  should  not  be  memorized,  the  ideas 
which  they  express  should  be  thoroughly  understood. 

78.  Since  6  times  7  ft.  =  42  ft.,  42  ft.  -5-  7  ft.  =  6,  and 
42  ft.  ^  6  =  7  ft.     It  is  therefore  clear  that 

1.  If  the  dividend  and  divisor  are  concrete  numbers,  the  quo- 
tient is  an  abstract  number  ;  and 

2.  If  the  dividend  is  concrete  and  the  divisor  abstract,  the  quo- 
tient is  a  concrete  number  like  the  dividend. 

In  §106  it  will  be  seen  thgit  there  are  two  kinds  of  division:  42  ft. -4-  7  ft.  = 
6  is  sometimes  called  measuring,  because  42  ft.  is  measured  by  7  ft. ;  42  ft.  -^ 
6  =  7  ft.  is  sometimes  called  partition,  because  42  ft.  is  divided  into  6  equal 
parts. 

62 


DIVISIOK  53 

ORAL  EXERCISE 

1.  Divide  by  2 :  18,  32,  78,  450,  642,  964,  893. 

2.  Divide  by  3 :  27,  67,  72,  423,  642,  963,  845. 

3.  Divide  by  4:  64,  88,  92,  488,  192,  396,  728. 

4.  Divide  by  5:  65,  85,  95,  135,  275,  495,  725. 

5.  Divide  by  6 :  84,  96,  54,  246,  546,  672,  846,  636. 

6.  Divide  by  7 :  63,  84,  91,  217,  497,  714,  791,  921. 

7.  Divide  by  8 :  72,  56,  88,  248,  640,  128,  144,  152. 

8.  Divide  by  4 :  56,  96,  77,  241,  168,  128,  920,  848. 

9.  Divide  by  6 :  78,  96,  56,  272,  848,  190,  725,  966. 
10.  Divide  by  9 :  98,  72,  49,  279,  819,  720,  189,  918. 

ORAL   EXERCISE 

1.  16  ft.  --  2  =  ?  24  ft.  -^  8  ft.  =  ? 

2.  $25  -i-  5  =  ?     129.75  --  5  =  ?   1129.78  --  9  =  ?  13.40  -- 
4  =  ? 

3.  126  yd. -4- 3  yd.  =  ?    1125-^25  =  ?     16.25 -^  $1.25  =  ? 

4.  If  9  T.  of  coal  cost  $49.50,  what  is  the  cost  per  ton? 

Solution.    $49.50  -f-  9  =  $5 ;  subtracting  9  times  |5,  the  re-  $5.50 

suit  is  $4.50  undivided;    $4.50  h- 9  =  $0.50.      Therefore  the  a\WJorT7i 

quotient  is  $5.50.  y;*4y.^U 

5.  At  $  1. 75  a  yard,  how  many  yards  can  be  bought  for  $  35  ? 

Solution.    The  divisor  contains  cents    and    it  is  therefore  20 

better  to  first  change  both  dividend  and  divisor  to  cents.     It  is 


found  that  $35  would  buy  20  times  as  many  yards  as  $1.75  ,  or  -^ 

20  yd. 

6.  If  5  T.  of  coal  cost  $31.25,  what  is  the  cost  per  ton? 

7.  At  $  2.50  per  yard  how  many  yards  can  be  bought  for  $  550  ? 

ORAL  EXERCISE 

1.  How  many  weeks  in  98  da.  ? 

2.  What  is  ^^  of  2250  bbl.  of  apples?  Jg?  i?  ^\? 

3.  The  quotient  is  8  and  the  dividend  128.      What  is  the 
divisor  ? 

4.  How  many  times  can  18  be  subtracted  from  75,  and  what 
will  remain? 


54  CONCISE   BUSINESS   ARITHMETIC 

5.  At  15^  per  pound,  how  many  pounds  of  beef  can  be 
bought  for  $6.30? 

6.  The  quotient  is  5,  the  divisor  23,  and  the  remainder  2. 
What  is  the  dividend  ? 

7.  If  5  men  earn  $17.50  a  day,  how  much  can  8  men  earn 
in  2  da.  at  the  same  rate? 

8.  What  is  the  nearest  number  to  150  that  can  be  divided 
by  9  without  a  remainder? 

9.  If  there  are  960  sheets  in  40  qr.   of  paper,  how  many 
sheets  in  5  qr.  ?  in  11  qr.  ? 

10.  If  6  bbl.  of  apples  are  worth  $21,  what  are  24  bbl.  worth 
at  the  same  rate  ?  36  bbl.  ? 

11.  If  17  bbl.  of  flour  cost  $85,  what  will  25  bbl.  cost  at  the 
same  rate  ?  32  bbl.  ?  48  bbl.  ?  34  bbl.  ? 

12.  If  8  be  added  to  a  certain  number,  7  can  be  subtracted 
from  that  number  7  times.    What  is  the  number  ? 

13.  If  20  yd.  of  cloth  cost  $60,  for  how  much  per  yard 
must  it  be  sold  to  gain  $25?   to  gain  $15? 

14.  A  grocer  sold  250  oranges  at  5^  each  and  gained  $5. 
How  much  did  he  pay  a  dozen  for  the  oranges? 

15.  A  grocer  pays  $3  for  20  doz.  of  eggs.  At  what  price  per 
dozen  must  he  sell  them  in  order  to  gain  $1.50? 

16.  At  $2.50  per  yard,  how  many  yards  of  cloth  can  be 
bought  for  $75?  for  $150?  for  $2500?  for  $750? 

17.  How  many  days'  labor  at  $3.50  per  day  will  pay  for  2  T. 
of  coal  at  $7  a  ton  and  5  lb.  of  tea  at  70^ per  pound? 

18.  A  clothier  pays  $96  for  a  dozen  overcoats.  At  how 
much  apiece  must  he  retail  them  to  gain  $48  on  the  lot? 

19.  A  man  exchanged  1140  bu.  of  wheat  at  $1  per  bushel 
for  flour  at  $6  per  barrel.     How  many  barrels  did  he  receive? 

20.  It  was  found  that  after  15  had  been  subtracted  5  times 
from  a  certain  number  the  remainder  was  4.  What  was  the 
number? 

21.  A  man  contracts  a  debt  of  $175  which  he  promises  to 
pay  in  weekly  installments  of  $3.50  each.  After  paying  $35, 
how  many  more  payments  has  he  to  make? 


DIYISIOK  55 

79.   Examples,     i.   Divide  4285  by  126. 

Complete  Operation  Required  Work 

34^lg  Mjl^ 

126)4285  126)4285 

378           =3  times  126  378 

505  undivided  505 

604          =4  times  126  604 

1  undivided  1 


Check.     34  x  126  +  1  =  4285 

The  remainder  cannot  always  be  written  as  a  part  of  the  quotient.     Thus 

in  the  problem,  "  At  $7  per  head  how  many  sheep  can  be  bought  for  $37," 
we  cannot  say,  "  5f  sheep,"  but  "  5  sheep  and  f  2  remaining." 

2.   A  farmer  received  $283.25  in  payment  for  275  bu.  of  wheat. 
How  much  was  received  per  bushel  for  the  wheat? 

$1.03 

Solution.      $283.75 -- 275  =  $1   and  §8.25  undivided.        275)$283.25 
$8.25 -J- 275  =  $0.03.     $1.03  per  bushel  was  therefore  re-  eync 

ceived  for  the  wheat.  —        • 

Check.     275  times  $1.03  =  §283.25.  ° -^^ 

8  25 

80.  Work   in   division   may  be    abridged   by   omitting   the 
partial  products  and  writing  only  the  partial  dividends. 

81.  Example.     Divide  S614.80  by  232. 

Solution.     Omit  writing  the  products;   subtract  mentally  and  write  the 
remainder  only  :   2  x  232  =  464  ;  464  subtracted  from  614 
equals  150  ;  omit  the  writing  of  the  464.    Proceed  as  follows : 

2  times  2  plus  0  =  4;  2  times  3  plus  5  =11.    2  times  2  + 1  =  5,  232)  S  614.80 

and  5  plus  1  =  6.     Bring  down  8.     6  times  2  plus  6  =  18 ;  150  8 

6  times  3  plus  1  =  19,  and  19  + 1  =  20  ;  6  times  2  plus  2  =  14,  1160 

and  14  plus  1  =  15.    Bring  down  0  and  proceed  as  before.  0  00 

WRITTEN   EXERCISE    ' 

1.  Find  the  cost  of  8800  lb.  of  oats  at  45/  per  bushel  of  32  lb. 

2.  How  many  automobiles,  at  $650  each,  can  be  purchased 
for  84,225,000? 

3.  By^  what  number  must  8656  be  multiplied  to  make  the 
product  8,223,200? 


S2.65 


56 


CONCISE   BUSINESS   AEITHMETIC 


4.  If  120  bbl.  of  flour  cost  $660,  what  will  829  bbl.  cost  at 
the  same  rate  ? 

5.  The  product  of  two  numbers  is  1,928,205.  If  one  of  them 
is  621,  what  is  the  other  ? 

6.  If  380  T.  of  coal  can  be  bought  for  $3040,  how  many 
tons  can  be  bought  for  $3600  ? 

7.  How  many  cords  of  128  cu.  ft.  in  a  pile  of  wood  con- 
taining 235,820  cu.  ft.  ?     What  is  it  worth  at  $4.50  per  cord  ? 

8.  A  speculator  sold  a  quantity  of  apples  that  cost  $2500 
for  $4750.  If  his  gain  per  barrel  was  $1.12^,  how  many 
barrels  did  he  buy  ? 

9.  A  man  received  a  legacy  of  $11,375  which  he  invested 
in  railroad  stock.  He  paid  a  broker  $125  to  buy  stock  at 
$112.50  per  share.     How  many  shares  were  bought  ? 

10.  A  dealer  bought  250  T.  of  coal  by  the  long  ton  of  2240  lb. 
at  $  6.50  per  ton.  He  retailed  the  same  at  $  8.25  per  short  ton  of 
20001b.    What  was  the  total  gain  ? 

11.  In  a  recent  year  there  were  produced  in  the  United  States 
730,627,000  bu.  of  wheat  on  45,814,000  A.  What  was  the  yield 
per  A.  ?    What  was  the  total  yield  worth  at  90/  per  bu.  ? 

12.  Copy  and  complete  the  following  table  of  corn  statistics. 
Check  the  work.  (The  total  yield  multiplied  by  the  price  per 
bushel  should  .equal  the  total  valuation.) 

Principal  Corn-growing  States  in  a  Hecent  Year 


State 

Yield  in  Bushels 

Farm  Price 
PER  Bushel 

Farm  Valuation 

Illinois 

Iowa 

Nebraska 

Missouri 

Indiana 

Kansas 

426  320  000 

? 

? 

? 
199  364  000 
174  225  000 

62^ 

62^ 
62j? 
62)? 
62ji 

264  318  400 
267  853  020 
113  221920 
151  220  480 

? 

? 

Total 

? 

m<f' 

p 

13-15.  Make  and  solve  three  self -checking  problems  in  division. 


BIYISIOK  57 

SHORT   METHODS   IN  DIVISIOK 

Powers  and  Multiples  of  10 

oral  exercise 

1.  How  many  times  is  10  contained  in  50  ?  100  in  800? 
1000  in  9000? 

2.  Cutting  off  a  cipher  in  30  divides  it  by  what  number? 

3.  Cutting  off  two  ciphers  in  800  divides  it  by  what  number? 

4.  Cutting  off  three  ciphers  in  11,000  divides  it  by  what 
number  ? 

5.  Read  aloud,  supplying  the  missing  words : 

a.  The  number  of  lO's  in  any  number  may  be  found  by 
cutting  off  the  units'  figure ;  the  number  of  lOO's  by  cutting 

off  the and figures ;  the  number  of  by  cutting 

off  the  hundreds'  and  tens'  and  units'  figures. 

h.    In  4561  there  are  456  tens  and  1  unit,  or  456  J^  tens ;  45 

and  61  units,  or  45^^^^  hundreds ;  and thousands  and 

561  units,  or  4^^q6_L-  thousands. 

6.  How  many  times  is  $0.10  contained  in  f  1  ?  fO.Ol  in 
fl?  $0,001  in  $1? 

7.  What  is  Jo  of  $1?     -jloof^l?     lAoofll? 

8.  Read  aloud,  supplying  the  missing  words:  10.60  is 

of  $6  ;  $0.06  is of  $6  ;     $0,006  is of  $6. 

9.  Formulate  a  short  method  for  dividing  United  States 
money  by  10 ;  by  100  ;  by  1000. 

10.  By  inspection  find  the  quotient  of  : 

a.   736 -f- 10.  e,  $271-5-100.         ^.  2140  lb.  ^  100. 

h.    1531-^100.  /  $519.50-10.     j.  3145  lb. -^  100. 

c.  16351 -f- 1000.         ^.$84.50-100.     A?.  3416  ft.  -!- 1000. 

d,  311219-10000.     h,  $2150-1000.     I.  1279  posts -^  100. 

11.  Read  aloud,  supplying  the  missing  amounts : 
a.    6400-1600  = ;  640-^10  = . 

h.    27000-5-9000  = ;    2700^900= ;    270-^90  = 

;  27 --9= . 


18801  --  90  = --9;  214200  -^  700  =  2142 


58  CONCISE   BUSINESS   ARITHMETIC 

12.  Ho\^  is  the  quotient  affected  by  like  changes  in  both 
the  dividend  and  divisor  ? 

13.  Divide  1323  by  400. 

Solution.     Cut  off  the  two  ciphers  in  the  divisor  and  two  ^il^ 

digits  in  the  right  of  tlie  dividend,  thus  dividing  both  dividend  4|00^13I23 
and  divisor  by  100.     4  is  contained  in  13  tliree  times  witli  a     '         -j  ^ 
remainder  1  hundred.     Adding  to  this  remainder  the  23  units  _ 

remaining  in  the  dividend  after  dividing  by  100,  the  true  re-  123 

mainder  is  123, which  write  in  fractional  form. 

14.  Eead  aloud,  supplying  the  missing  amounts  :  1611  -j-  400 

= ;    2847-^700  = ;    1531-^-300  = ;    16139-^ 

4000  = . 


15.  Formulate  a  rule  for  dividing  a  number  by  any  multiple 
of  ten. 

16.  State  the  quotient  of  : 

a.    1231-^30.     /.  96131 -f- 400.  h.  63571-^3000. 

h.    9647^40.     g.   84199-^700.  Z.  16657^4000. 

c,    6551 --50.     h.   64137-800.  m.  36119-^6000. 

(f.  4273^70.     i.   45117-^900.  n,  18177-5-9000. 

e.    8197 -f- 90.     j,    25121-^-500.  o.  42113-^7000. 

ORAL  REVIEW  EXERCISE 

The  diagram  on  the  opposite  page  is  a  portion  of  the  New  York  Central 
time-table  giving  the  distances  between  many  of  the  stations  from  New 
York  City  to  Suspension  Bridge,  and  the  time  taken  by  two  different  trains 
to  travel  this  route.  • 

1.  How  many  miles  between  New  York  City  and  Pough- 
keepsie?  between  Poughkeepsie  and  Utica?  between  Utica  and 
Syracuse?  between  Syracuse  and  Rochester?  between  Rochester 
and  Buffalo?  between  Buffalo  and  Niagara  Falls? 

2.  What  is  the  distance  between  New  York  City  and  Syra- 
cuse? between  Poughkeepsie  and  Niagara  Falls?  between 
Rochester   and   Suspension   Bridge? 

3.  How  many  miles  between  Ludlow  and  each  station  below 
it?  between  Poughkeepsie  and  each  station  below  it?  between 
Tarry  town  and  each  station  below  it? 


DIVISION 


59 


4.  How  many  miles  between   Montrose  and  each  station 
below  it?   between  Oscawana  and 
each  station  below  it? 

5.  At  2^  per  mile,  what  is  the 
fare  from  New  York  to  Niagara 
Falls?  from  Poughkeepsie  to  Syra- 
cuse ?  from  Buffalo  to  Utica  ?  from 
Troy  to  Yonkers? 

6.  At  2j^  per  mile,  what  is  the 
fare  from  Rochester  to  Syracuse? 
from  Rensselaer  to  Suspension 
Bridge?  from  Albany  to  Niagara 
Falls?  from  Syracuse  to  Buffalo? 
to  Albany? 

7.  How  long  does  it  take  train 
No.  93  to  travel  the  first  30  mi. 
toward  Poughkeepsie?  the  first  74 
mi.  toward  Albany? 

8.  How  long  is  train  No.  93 
in  making  the  run  from  Fishkill 
Landing  to  Camelot?  This  is  ap- 
proximately how  many  miles  an 
hour? 

9.  How  long  does  it  take  train 
No.  73  to  make  the  run  from  Utica 
to  Syracuse  ?  How  long  does  it  take 
train  No.  73  to  make  the  run  from 
Fishkill  Landing  to  Chelsea  ?  This 
is  approximately  how  many  miles 
an  hour? 

10.  Add  each  number  in  the  col- 
umn marked  "Miles"  to  the  one 
immediately  below  it. 

Thus,  9, 12, 16, 24, 34, 45,  58,  etc.  In  add- 
ing 89  and  95  think  of  179  and  5,  or  184 ;  in 
adding  143  and  149  think  first  of  243  and  49  and  then  of  283  and  9,  or  292. 

CB 


"zn 

NORTH 

Ip 

1 

AND 
WEST  BOUND 

1^ 

bCJ5 

s 

73 

93 

New  York 

0 

Grand  Cent.  Sta Lv. 

121110 

6t01 

4 

125th  St.  Sta " 

12A23 

6,*,13 

5 

138th  St.  Sta " 

6.15 

7 

High  Bridge " 

< 

6.21 

8 

Morris  Heights " 

6.25 

10 

Kings  Bridge  " 

6.29 

11 

Spuyten  Duyvil " 

Jii 

6.33 

1« 

Riverdale " 

« 

14 

Mt.  St.  Vincent " 

r% 

15 

Ludlow " 

16 

Yonkers " 

12  46 

6.43 

18 

Glenwood '• 

6.46 

20 

Hastings-on-Hudson  " 

6.52 

21 

Dobbs'  Ferry " 

Ardsley- on -Hudson  " 

6.59 

22 

7.01 

23 

Irvington " 

7.05 

26 

Tarrytown " 

1.09 

7.12 

30 

Scarborough " 

7.19 

31 

Ossining •' 

1.25 

7.25 

35 

Croton-on-Hudson  .  " 

7.31 

37 

Oscawana " 

7..34 

38 

Crugers " 

7.37 

;«) 

Montrose " 

7.41 

42 

Peekskill «* 

1.47 

7.49 

47 

Highlands " 

7.59 

50 

Garrison " 

% 

8.06 

53 

Cold  Spring " 

X 

8.12 

56 

Storm  King ♦' 

8.16 

58 

Dutchess  June " 

8.21 

59 

Fishkill  Landing " 

2.24 

8.27 

63 

Chelsea " 

2.31 

8.34 

65 

New  Hamburg " 

8.40 

69 

Camelot " 

8,46 

74 

Poughkeepsie Ar. 

2.53 

8A55 

74 

80 

84 

89 

95 

99 

105 

109 

111 

115 

Poughkeepsie Lv. 

Hyde  Park " 

Staatsburgh " 

Rhineclitf  (Rh'b'k)..  " 

Barrytown " 

Tivoli " 

Gerraantown " 

Linlithgo " 

Greendale " 

Hudson " 

3.05 

4.47 

119 
122 
125 

Stockport " 

Newton  Hook " 

Stuyvesant " 

131 
135 
142 
143 

Schodack  Landing..  " 

Castleton " 

Rensselaer " 

Albany Ar. 

5.50 

149 

Troy.„ " 

6^ 

238 

[Jtica Ar. 

8/)40 

291 

Syracuse " 

9.55 

371  Rochester " 

11.38 

440  Buffalo " 

U15 

463  Niagara  Falls Ar. 

?r^^ 

464 1  Suspension  Bridge " 

2520 

60  CONCISE   BUSINESS   ARITHMETIC 

11.  Multiply  each  number  in  the  column  marked  "Miles" 
by  5;  by  8;  by  3 ;  by  7;  by  6 ;  by  4;  by  9. 

The  numbers  in  the  portion  of  the  time-table  illustrated  may  be  used 
for  such  other  exercises  as  may  seem  necessary  at  this  point.  Students 
should  be  impressed  with  the  importance  of  being  able  to  add,  subtract, 
multiply,  and  divide  numbers  in  any  relative  position. 

12.  Five  parts  of  120  are  15,  18,  32,  10,  and  20.  Find  the 
sixth  part,  and  multiply  it  by  15. 

13.  From  a  flock  of  170  sheep  I  sold  at  different  times  12, 
18,  32,  and  9.     How  many  sheep  remained  ? 

14.  Multiply  by  11  each  of  the  following  numbers:  21,  32, 
43,  54,  65,  76,  87,  98,  61,  28,  37,  14,  21,  62. 

15.  At  22  /  per  yard,  what  will  18  yd.  cost  ?  21  yd.  ?  36  yd.  ? 
56  yd.  ?  29  yd.  ?  73  yd.  ?  94  yd.  ?   72  yd.  ? 

16.  Multiply  each  number  in  problem  15  by  33  ;  by  44. 

WRITTEN   REVIEW   EXERCISE 

1.  Find  the  total  cost  of  the  articles  in  problem  3  of  the 
oral  exercise,  page  42.  Fmd  the  total  of  the  products  in  the 
oral  exercise,  page  46. 

2.  A  mechanic  earns  $125  per  month  and  his  monthly  ex- 
penses average  $72.  If  he  saves  the  remainder,  how  long  will 
it  take  him  to  save  $4352  ? 

3.  I  spent  $24,800  for  apples  at  $2.50  per  barrel.  The  loss 
from  decay  was  equal  to  74  bbl.  What  was  my  gain,  if  the 
remainder  of  the  apples  sold  for  $3.75  per  barrel,  and  my 
expenses  for  storage  were  $675.80? 

4.  During  a  certain  week  a  contractor  employed  help  as 
follows:  34  hands,  8  hr.  per  day,  for  5  da.,  at  15/  per  hour; 
16  hands,  9  hr.  per  day,  for  6  da.,  at  25/  per  hour;  29  hands, 
10  hr.  per  day,  for  6  da.,  at  18 /per  hour.     Find  the  amount  due. 

5.  In  a  recent  year  there  were  produced  on  37,917,000  A. 
in  the  United  States  1,418,337,000  bu.  oats,  valued  on  the  farm 
at  31.3/  per  bushel.  What  was  the  average  yield  per  acre? 
What  was  the  value  of  the  year's  crop? 


DIVISION 


61 


6.  Without  copying  find  (a)  the  total  number  of  railway 
employees  in  the  United  States  in  1910  and  (h)  the  total  num- 
ber per  one  hundred  miles  of  hue  in  the  same  year. 


Railway  Employees  in  the  United  States 


1910 

1911 

Class 

Total 
Number 

Number 

PER 

100  Ml. 

Average 
Daily 
Wages 

Total 
Number 

Number 

PER 

100  Mi. 

Average 
Daily 
Wages 

General  officers 

5.476 

2 

$13.27 

5,628 

2 

$12.99 

Other  officers 

9,392 

4 

6.22 

10,196 

4 

6.27 

General  office  clerks 

76,329 

32 

2.40 

76,513 

31 

2.49 

Station  agents 

37,379 

16 

2.12 

38,277 

16 

2.17 

Other  station  men 

153,104 

64 

1.84 

153,117 

62 

1.89 

Engineers 

64,691 

27 

4.55 

63,390 

26 

4.79 

Firemen 

68,321 

28 

2.74 

66,376 

27 

2.94 

Conductors 

48,682 

20 

3.91 

48,200 

20 

4.16 

Other  trainmen 

136,938 

57 

2.69 

133,221 

64 

2.88 

Machinists 

55,193 

23 

3.08 

55,207 

22 

3.14 

Carpenters 

68,085 

28 

2.51 

65,989 

27 

2.54 

Other  shopmen 

225,196 

94 

2.18 

226,785 

92 

2.24 

Section  foremen 

44,207 

18 

1.99 

44,466 

18 

2.07 

Other  trackmen 

378,955 

157 

1.47 

363,028 

147 

1.50 

All  other  employees 

229,806 

95 

2.01 

227,779 

93 

2.08 

7.  Without  copying  find  (a)  the  total  number  of  railway 
employees  in  the  United  States  in  1911  and  (5)  the  total  num- 
ber per  one  hundred  miles  of  line  in  the  same  year. 

8.  Find  the  total  salaries  paid  to  railway  employees  in  1910  ; 
in  1911. 

9.  Find  the  average  daily  wages  paid  to  railway  employees 
in  1910;  in  1911. 

10.    In  a  recent  year  four  leading  railway  systems  had  out- 
standing bonds  as  follows : 

a.  8761,963,000.  c.  $1,096,773,410. 

b.  $576,300,000.  d.  $428,649,000. 
Find  the  average  amount  of  the  bonds  outstanding. 


62  CONCISE   BUSINESS   AEITHMETIC 

WRITTEN  REVIEW 

In  these  problems  divide  across,  and  then  add  the  dividend  column 
and  the  quotient  column.  Check :  divide  the  total  of  the  dividend 
column  by  the  divisor,  and  this  quotient  should  equal  the  sum  of  the 

individual  quotients.  Time,  approximately,  fifteen  minutes, 

1.  2.  3. 

36-^4  =  ?  45-^5  =  ?  m^Q^'i 

48-f-4  =  ?  75-5-5  =  ?  72-f-6  =  ? 

56-f-4  =  ?  95-5-5  =  ?  84-^6  =  ? 

24-^4  =  ?  Q^-^b^"^  78-5-6  =  ? 

84-4-4  =  ?  35-f-5  =  ?  48-f-6  =  ? 

44-4-4  =  ?  55-4-5  =  ?  36-5-6  =  ? 

64-4-4  =  ?  15-5-5  =  ?  54-4-6  =  ? 

76^4  =  ?  ^-^^=^1  1?-^?.=Z 

?  -4-4  =  ?  ?  -4-5  =  ?  ?  -^6  =  ? 

4.  5.  6. 

98-5-7  =  ?  88-4-2  =  ?  .    48-4-3  =  ? 

84-4-7  =  ?  76-^2  =  ?  54-5-3  =  ? 

63-4-7  =  ?  58-5-2  =  ?  69-4-3  =  ? 

49-5-7  =  ?  64-4-2  =  ?  72-4-3  =  ? 

91-4-7  =  ?  82-4-2  =  ?  84^3  =  ? 

56-5-7  =  ?  94-2  =  ?  93-4-3  =  ? 

77-5-7  =  ?  52-^2  =  ?  87-4-3  =  ? 

42-4-7  =  ?  Ii-^?  =  ?  ^^5=Z 

?-5-7  =  ?  ?-5-2  =  ?  ?^3  =  ? 

7.  8.  9. 

126-5-2  =  ?  144-5-4  =  ?  129-4-3  =  ? 

152^2  =  ?  124-4-4  =  ?  114-4-3  =  ? 

134-4-2  =  ?  152-4-4  =  ?  108-5-3  =  ? 

168-^2  =  ?  148-5-4  =  ?  147-5-3  =  ? 

184^2  =  ?  176-5-4  =  ?  189-4-3  =  ? 

156-4-2  =  ?  184-5-4  =  ?  165-5-3  =  ? 

172^2  =  ?  136-5-4  =  ?  195-4-3  =  ? 

138-4-2  =  ?  l^-^i  =  Z  138-5-3  =  ? 

?    -4-2  =  ?  ?    -5-4  =  ?  ?    -*-3  =  ? 


DIVISION.     U.S.   POSTAL   SERVICE  63 

82.  All  mailable  matter  for  transmission  by  the  United  States 
mails  within  the  United  States  or  to  Cuba,  Mexico,  Hawaii,  Porto 
Rico,  Canada,  and  the  Philippine  Islands  is  divided  into  four 
classes :  first-,  second-,  third-,  and  fourth-class  matter. 

First-class  matter  includes  letters,  postal  cards,  and  anything 
sealed  or  otherwise  closed  against  inspection.  The  rate  for  first- 
class  matter  is  2/  per  ounce  or  fraction  thereof;  for  a  postal 
card,  1  / ;  for  a  reply  postal  card,  2  /.  Written  or  typewritten 
matter  is  of  the  first  class,  whether  sealed  or  unsealed. 

Second-class  matter  mcludes  newspapers  and  periodicals  entirely 
in  print.  When  sent  by  publishers  or  news  agents,  the  rate  is 
1  /  per  pound  or  fraction  thereof ;  when  sent  by  others,  1  /  for 
each  4  oz.  or  fraction  thereof. 

Third-class  matter  mcludes  books  and  catalogues  (weighing 
8  oz.  or  less),  circulars,  pamphlets,  proof  sheets  and  manuscript 
copy  accompanying  tlie  same,  and  engravings.  The  rate  is  1/ 
for  each  2  oz.  or  fraction  thereof.     The  limit  of  weight  is  4  lb. 

All  postal  matter  of  the  first,  second,  or  third  class  may  be 
registered  at  the  rate  of  10/  for  each  package  in  addition  to  the 
regular  rates  of  postage. 

The  rates  on  special  delivery  letters  are  10  /  per  letter  in  addition 
to  the  regular  postage.  Any  matter  on  which  a  special  delivery 
stamp  is  affixed  is  entitled  to  special  delivery  within  certain  limits. 

Foreign  rates  of  postage  are  as  follows :  letters,  5/  per  ounce  for 
the  first  ounce,  and  3  /  for  each  additional  ounce.  (Double  rate 
is  charged  at  delivery  office  for  any  deficiency  in  prepayment.) 
Postal  cards,  2/  each;  newspapers  and  other  printed  matter, 
1/  for  2  oz. 

Some  foreign  countries,  as  Germany  and  Great  Britain,  come 
under  the  letter  rate  of  2  /  per  ounce. 

All  fourth-class  matter  is  now  included  in  the  domestic  parcel 
post,  by  a  law  which  became  effective  January  1, 1913.  The  fol- 
lowing are  some  of  the  principal  features  of  this  law : 

The  country  is  divided  into  zones,  the  rate  of  postage  being  dependent  on 
the  zone  where  the  parcel  is  to  be  delivered.  The  zone  center  is  the  point 
of  mailing.     Regular  postage  stamps  are  used  on  parcel-post  packages. 


64 


CONCISE   BUSIKESS   AEITHMETIC 


Parcels  weighing  4  oz.  or  less  are  mailable  at  the  rate  of  1^  for  each 
ounce  or  fraction  of  an  ounce,  regardless  of  distance.  Parcels  weighing 
more  than  4  oz.  are  mailable  at  the  pound  rates  shown  in  the  table,  a 
fraction  of  a  pound  being  considered  as  a  full  pound. 

Books  and  catalogues  weighing  in  excess  of  8  oz.  may  be  sent  by  parcel  post. 

The  weight  limit  for  zones  1  and  2  is  50  lb. ;  for  all  the  other  zones,  20  lb. 

The  local  rate  applies  to  parcels  to  be  delivered  at  the  office  of  mailing, 
or  on  a  rural  route  starting  from  that  office. 

A  parcel  may  be  insured  against  loss  to  the  amount  of  its  actual  value 
not  exceeding  $50. 

A  special  delivery  of  a  parcel  will  be  made  on  the  payment  of  an  addi- 
tional 10  f,  at  the  mailing  office. 

In  the  table,  the  rates  are  complete  up  to  11  lb.  From  this  point  on  only 
illustrative  weights  and  rates  are  given ;  omissions  are  indicated  by  stars. 

The  local  post  office  can  furnish  a  parcel-post  map  of  the  United  States 
showing  the  regions  included  in  the  different  zones. 


50  mi. 

50- 
150  mi. 

150- 
SOOmi. 

300- 
600  mi. 

600- 
lOOOmi. 

1000- 
1400  mi. 

1400- 
1800  mi. 

All  over 
1800  mi. 

First  Zone 

Second 
Zone 
Rate 

Third 
Zone 
Rate 

Fourth 
Zone 
Rate 

Fifth 
Zone 
Rate 

Sixth 
Zone 
Rate 

Seventh 
Zone 
Rate 

Eighth 

Weight 

Local 
Rate 

Zone 
Rate 

Zone 
Rate 

lib. 

$0.05 

$0.05 

$0.05 

$0.06 

$0.07 

$0.08 

$0.09 

$0.11 

$0.12 

21b. 

.06 

.06 

.06 

.08 

.11 

.14 

.17 

.21 

.24 

31b. 

.06 

.07 

.07 

.la 

.15 

.20 

.25 

.31 

.36 

41b. 

.07 

.08 

.08 

.12 

.19 

.26 

.33 

.41 

.48 

51b. 

.07 

.09 

.09 

.14 

.23 

.32 

.41 

.51 

.60 

61b. 

.08 

.10 

.10 

.16 

.27 

.38 

.49 

.61 

.72 

71b. 

.08 

.11 

.11 

.18 

.31 

.44 

.57 

.71 

.84 

81b. 

.09 

.12 

.12 

.20 

.35 

.50 

.65 

.81 

.96 

91b. 

.09 

.13 

.13 

.22 

.39 

.56 

.73 

.91 

1.08 

101b. 

.10 

.14 

.14 

.24 

.43 

.62 

.81 

1.01 

1.20 

111b. 

.10 

.15 

.15 

.26 

.47 

.68 

.89 

1.11 

1.32 

*  *  * 

*  *  * 

*  *  * 

*  *  * 

*  *  * 

«  «  « 

*  *  * 

*  *  * 

«  «  « 

*  *  * 

151b. 

.12 

.19 

.19 

.34 

.63 

.92 

1.21 

1.51 

1.80 

»  *  * 

*  *  * 

*  *  * 

*  *  ^ 

«  «  « 

*  *  * 

*  *  * 

*  *  * 

«  «  « 

«  «  « 

201b. 

.15 

.24 

.24 

.44 

.83 

1.22 

1.61 

2.01 

2.40 

«  «  « 

*  *  * 

*  *  * 

*  *  * 

301b. 

.20 

.34 

.34 

«  «  « 

«  «  « 

«  «  « 

«  «  « 

401b. 

.25 

.44 

.44 

«  «  « 

*  *  * 

*  *  * 

*  *  * 

501b. 

.30 

.54 

.54 

DIVISION.    U.   S.   POSTAL   SERVICE  65 


ORAL    EXERCISE 

1.  What  is  the  postage  on  a  letter  weighing  i-  oz.  ?  4|  oz.  ? 
11  oz.  ?  3J  oz.  ?  2^  oz.  ?  41  oz.  ? 

2.  What  will  be  the  cost  of  postage  on  the  following  articles  at 
your  post  office  to  points  within  the  United  States :  an  ordinary- 
letter  weighing  2|  oz. ;  a  registered  letter  weighing  1^  oz. ;  a 
bundle  of  papers  weighing  10  oz.  ? 

3.  Find  the  total  cost  of  postage  on  the  following  to  points 
within  the  United  States:  a  special  delivery  letter  weighing  1^  oz.; 
some  printers'  proofs  weighing  18  oz. ;  some  separate  matter  for 
the  printer  weighing  12  oz. ;  a  pamphlet  weighing  6  oz. 

4.  Use  a  zone  map  and  find  the  cost  of  mailing  each  of  the 
following  articles : 

Article  Weight  Destination 

A  pair  of  opera  glasses  2  lb.    8  oz.  Kansas  City,  Mo. 

A  pair  of  ladies'  gloves  6  oz.  Indianapolis,  Ind. 

A  copy  of  Star-Land  1  lb.    8  oz.  Macon,  Ga. 

A  copy  of  Whittier's  Poems  1  lb.  12  oz.  Pittsburgh,  Pa. 

A  copy  of  Lowell's  Poems  1  lb.  10  oz.  Denver,  Colo. 

A  box  of  merchandise  3  lb.    8  oz.  Chicago,  111. 
A  box  containing  a  pair  of 

shoes  3  lb.    6  oz.  Austin,  Tex. 

A  piece  of  hardware  6  lb.    9  oz,  Detroit,  Mich. 

5.  A  publisher  sends  20,000  copies  of  his  magazine  by  mail. 
If  each  magazine  and  wrapper  weighs  14i  oz.  and  the  total 
number  is  weighed  at  the  post  office  in  bulk,  what  will  the 
publisher  have  to  pay  for  postage  ? 

6.  A  subscriber  mailed  two  copies  of  the  above  magazine  to  a 
friend.   What  was  the  cost  for  postage  ? 

7.  25,000  copies  of  a  monthly  magazine  weighing  14J  oz.  were 
sent  by  mail.    What  was  the  cost  to  the  publisher  for  postage  ? 

8.  Find  the  total  cost  for  mailing  the  following:  printers' 
proof  weighing  18^  oz. ;  manuscript  and  printers'  proof  in  one 
package,  weighing  28  i-  oz. ;  a  special  delivery  letter,  weighing  |  oz. 


66  CONCISE   BUSINESS   ARITHMETIC 

PKICE   LISTS   AND   INVENTORIES 

Price  Lists 

These  price  lists  are  to  he  used  in  making  out  the  inventories 
which  are  found  on  the  four  pages  following : 


Article 

1. 

2. 

3. 

4. 

5. 

Bedsteads 

$6.25 

$8.50 

$11.75 

$5.25 

$14.50 

Bookcases 

42.00 

38.00 

25.00 

35.00 

32.00 

Bureaus 

18.60 

27.25 

22.50 

16.50 

34.20 

Cabinets : 

China 

22.00 

20.00 

27.50 

32.50 

37.50 

Medicine 

2.25 

1.75 

2.50 

3.25 

2.75 

Music 

10.00 

11.00 

9.00 

8.60 

10.50 

Parlor 

25.50 

21.50 

25.00 

36.50 

38.00 

Chairs: 

Easy 

12.50 

10.50 

15.00 

22.25 

18.50 

Morris 

10.50 

12.25 

12.00 

9.75 

8.25 

Piano 

5.00 

6.50 

7.25 

9.00 

12.00 

Typewriter 

3.50 

4.50 

4.00 

5.60 

6.00 

Cheval  Mirrors 

20.00 

17.25 

18.50 

16.50 

21.25 

Chiffoniers 

24.00 

18.20 

31.75 

27.50 

40.00 

Davenports 

62.50 

50.00 

60.00 

45.50 

37.50 

Desks: 

Flat-top 

21.20 

17.60 

16.80 

22.30 

18.60 

Roll-top 

23.50 

21.25 

25.50 

27.25 

30.50 

Typewriter 

11.25 

12.25^ 

14.25 

10.25 

13.25 

Dinner  Trays 

5.50 

6.25 

7.25 

6.26 

8.25 

Footrests 

1.75 

1.50 

1.60 

2.00 

2.25 

Hall  Racks 

14.25 

13.50 

17.25 

18.50 

12.25 

Lounges 

25.00 

17.50 

21.50 

32.00 

23.50 

Mattresses 

11.40 

12.50 

13.25 

17.50 

21.00 

Ottomans 

5.25 

4.50 

4.25 

6.50 

4.75 

Parlor  Suites 

63.00 

52.50 

75.00 

67.50 

62.50 

Pillows 

2.50 

3.00 

3.50 

2.00 

3.25 

Sideboards 

60.00 

50.00 

45.00 

37.50 

72.50 

Tables : 

Dining 

21.50 

17.50 

22.60 

24.50 

25.00 

Dressing 

37.50 

32.25 

21.50 

35.25 

24.75 

Serving 

13.50 

11.00 

14.50 

10.50 

12.25 

Work 

10.00 

9.25 

9.00 

10.25 

11.00 

Wardrobes 

20.50 

25.25 

15.50 

21.76 

25.00 

Washstands 

6.00 

7.50 

5.50 

8.00 

10.50 

Each  inventory  may  be  worked  out  Jive  times,  using  the  above  price  lists. 
This  work  may  be  done  by  copying  the  data  and  making  the  extensions,  or  by 
making  the  extensions  only  and  then  totaling  each  inventory. 


WEITTEN  EEVIEW 


67 


7  Bureaus 
19  Bedsteads 

12  Chiffoniers 

5  Dressing  Tables 
21  Washstands 

8  Mattresses 
23  Pillows 

6  Bookcases 

3  Davenports 

13  Lounges 

17  Easy  Chairs 

7  Morris  Chairs 
5  Parlor  Suites 

8  Music  Cabinets 

12  Piano  Chairs 
15  Parlor  Cabinets 

5  Sideboards 

13  Dining  Tables 

8  China  Cabinets 

4  Serving  Tables 

9  Work  Tables 
12  Dinner  Trays 

4  Medicine  Cabinets 

8  Wardrobes 

11  Cheval  Mirrors 
15  Ottomans 

12  Footrests 

5  Hall  Racks 

6  Roll-top  Desks 
3  Flat-top  Desks 

9  Typewriter  Desks 
8  Typewriter  Chairs 


IirVENTOKIES 

2. 

8  Bureaus 

17  Bedsteads 

15  Chiffoniers  • 

3  Dressing  Tables 

18  Washstands 

11  Mattresses 
21  Pillows 

5  Bookcases 

4  Davenports 

12  Lounges 

20  Easy  Chairs 

3  Morris  Chairs 

6  Parlor  Suites 

10  Music  Cabinets 

11  Piano  Chairs 

21  Parlor  Cabinets 
2  Sideboards 

16  Dining  Tables 

5  China  Cabinets 

6  Serving  Tables 

7  Work  Tables 
15  Dinner  Trays 

8  Medicine  Cabinets 

5  Wardrobes 

14  Cheval  Mirrors 

12  Ottomans 

17  Footrests 

7  Hall  Racks 

4  Roll-top  Desks 
2  Flat-top  Desks 

10  Typewriter  Desks 

6  Typewriter  Chairs 


68 


CONCISE   BUSINESS   ARITHMETIC 


3. 

8  Bureaus 

15  Bedsteads 
14  Cliiffoniers 

4  Dressing  Tables 
19  Washstands 

12  Mattresses 

18  Pillows 

8  Bookcases 

5  Davenports 

16  Lounges 
22  Easy  Chairs 

6  Morris  Chairs 

7  Parlor  Suites 

11  Music  Cabinets 
14  Piano  Chairs 

12  Parlor  Cabinets 

6  Sideboards 

10  Dining  Tables 

7  China  Cabinets 

6  Serving  Tables 

8  Work  Tables 

11  Dinner  Trays 

7  Medicine  Cabinets 

9  Wardrobes 

13  Cheval  Mirrors 

19  Ottomans 

12  Footrests 

6  Hall  Racks 

8  Roll-top  Desks 
4  Flat-top  Desks 

14  Typewriter  Desks 
10  Typewriter  Chairs 


4. 

9  Bureaus 
13  Bedsteads 

11  Chiffoniers 

7  Dressing  Tables 

17  Washstands 
9  Mattresses 

23  Pillows 

6  Bookcases 

.  3  Davenports 
21  Lounges 

18  Easy  Chairs 

9  Morris  Chairs 
4  Parlor  Suites 
9  Music  Cabinets 

13  Piano  Chairs 
18  Parlor  Cabinets 

4  Sideboards 

12  Dining  Tables 
9  China  Cabinets 

5  Serving  Tables 
11  Work  Tables 

14  Dinner  Trays 

5  Medicine  Cabinets 

7  Wardrobes 

17  Cheval  Mirrors 

15  Ottomans 

18  Footrests 

3  Hall  Racks 

5  Roll-top  Desks 

6  Flat-top  Desks 

11  Typewriter  Desks 

7  Typewriter  Chairs 


WRITTEN  REVIEW 


69 


12  Bureaus 
23  Bedsteads 

13  Chiffoniers 

8  Dressing  Tables 

16  Washstands 

14  Mattresses 
22  Pillows 

4  Bookcases 
4  Davenports 

17  Lounges 

14  Easy  Chairs 
12  Morris  Chairs 

10  Parlor  Suites 
14  Music  Cabinets 
17  Piano  Chairs 
22  Parlor  Cabinets 

7  Sideboards 
14  Dining  Tables 

4  China  Cabinets 

11  Serving  Tables 

5  Work  Tables 

19  Dinner  Trays 

6  Medicine  Cabinets 

12  Wardrobes 

20  Cheval  Mirrors 

11  Ottomans 

21  Footrests 

4  Hall  Racks 

12  Roll-top  Desks 

5  Flat-top  Desks 

13  Typewriter  Desks 
12  Typewriter  Chairs 


14  Bureaus 
21  Bedsteads 

16  Chiffoniers 

11  Dressing  Tables 

14  Washstands 

15  Mattresses 

17  Pillows 

7  Bookcases 

7  Davenports 
19  Lounges 

25  Easy  Chairs 

11  Morris  Chairs 
9  Parlor  Suites 

12  Music  Cabinets 
21  Piano  Chairs 

16  Parlor  Cabinets 
9  Sideboards 

18  Dining  Tables 

6  China  Cabinets 
9  Serving  Tables 

10  Work  Tables 

13  Dinner  Trays 

10  Medicine  Cabinets 

15  Wardrobes 

16  Cheval  Mirrors 

19  Ottomans 

14  Footrests 

8  Hall  Racks 

9  Roll-top  Desks 
8  Flat-top  Desks 

7  Typewriter  Desks 

15  Typewriter  Chairs 


70 


CONCISE   BUSINESS  AEITHMETIC 


19  Bureaus 

21  Bedsteads 
11  Chiffoniers 

9  Dressing  Tables 

15  Washstands 

11  Mattresses 
24  Pillows 

9  Bookcases 
6  Davenports 

22  Lounges 

12  Easy  Chairs 

8  Morris  Chairs 

9  Parlor  Suites 
14  Music  Cabinets 

9  Piano  Chairs 
17  Parlor  Cabinets 

3  Sideboards 

13  Dining  Tables 

4  China  Cabinets 
11  Serving  Tables 
13  Work  Tables 
24  Dinner  Trays 

6  Medicine  Cabinets 

13  Wardrobes 

14  Cheval  Mirrors 

6  Ottomans 

8  Footrests 
11  Hall  Racks 

3  Roll-top  Desks 

7  Flat-top  Desks 

16  Typewriter  Desks 

9  Typewriter  Chairs 


8. 

17  Bureaus 

20  Bedsteads 
16  Chiffoniers 

6  Dressing  Tables 

21  Washstands 

15  Mattresses 
25  Pillows 
10  Bookcases 

2  Davenports 

16  Lounges 

8  Easy  Chairs 
13  Morris  Chairs 

3  Parlor  Suites 
10  Music  Cabinets 

7  Piano  Chairs 

22  Parlor  Cabinets 
5  Sideboards 

9  Dining  Tables 

10  China  Cabinets 
7  Serving  Tables 

17  Work  Tables 
21  Dinner  Trays 

9  Medicine  Cabinets 

11  Wardrobes 

18  Cheval  Mirrors 
9  Ottomans 

10  Footrests 

12  Hall  Racks 

2  Roll-top  Desks 
9  Flat-top  Desks 

10  Typewriter  Desks 

11  Typewriter  Chairs 


CHAPTER  yi 

CHECKING  RESULTS 

83.  It  has  been  seen  in  the  preceding  exercises  on  statis- 
tics, time  sheets,  etc.,  that  various  ruled  forms  provide  for  prac- 
tical and  convenient  methods  of  checking  results.  While  it  is 
possible  to  give  a  great  variety  of  these  problems  it  is  also 
necessary  to  give  a  great  many  problems  that  do  not  furnish 
such  a  check. 

84.  It  is  very  important  that  all  results  be  checked.  The 
most  common  methods  of  checking  addition,  subtraction,  and 
division  have  already  been  mentioned.  Multiplication  may 
be  proved  by  dividing  the  product  by  either  factor,  or  as 
explained  on  page  38. 

The  properties  of  9  and  11  may  also  be  applied  to  advan- 
tage in  checking  results,  especially  results  in  multiplication  and 
division. 

PROPERTIES  OF  9  AND  11 

Properties  of  9 

85.  Any  number  of  lO's  is  equal  to  the  same  number  of  9's 
plus  the  same  number  of  units ;  any  number  of  lOO's  is  equal 
to  the  same  number  of  99's  plus  the  same  number  of  units; 
any  number  of  lOOO's  is  equal  to  the  same  number  of  999's 
plus  the  same  number  of  units ;  and  so  on. 

Thus,  10  =  one  9  +  1 ;  40  =  four  9's  +  4 ;  100  =  one  99  +  1 ;  300  = 
three  99's  +  3 ;  500  =  five  99's  +  5. 

86.  Any  number  may  be  resolved  into  one  less  than  as  many 
•  multiples  of  10  as  it  contains  digits. 

Thus,  946  =  900  +  40  +  6 ;  42175  =  40000  +  2000  +  100  -1-70  +  6. 

71 


72  CONCISE   BUSINESS   ARITHMETIC 

87.  The  excess  of  9's  in  any  power  of  10  or  in  any  multiple 
of  a  power  of  10  is  the  saijie  as  the  significant  figure  (unless  that 
figure  is  9,  then  there  is  no  excess)  in  that  number.     Hence, 

The  excess  of  9's  in  any  number  is  equal  to  the  excess  of  9^s  in 
the  sum  of  its  digits. 

Thus,  the  excess  of  9's  in  241  =  2  +  4  +  1,  or  7.  The  excess  of  9's  in 
946  =  9  +  4  +  6,  or  19 ;  but  19  contains  9,  and  the  excess  of  9's  in  19  =  1  + 
9,  or  10 ;  but  10  contains  9,  and  the  excess  of  9's  in  10  =  1  +  0,  or  1 ;  the 
excess  of  9's  in  946  is  therefore  shown  to  be  1. 

88.  In  finding  the  excess  of  9's  in  any  number,  omit  all  9's 
and  all  combinations  of  two  or  three  digits  which  it  is  seen  at 
a  glance  will  make  9  or  some  multiple  of  9. 

Thus,  in  finding  the  excess  of  9's  in  9458,  begin  at  the  left,  reject  the 
first  digit  9,  the  sum  of  the  next  two  digits,  9,  and  the  single  8  will  be  the 
excess  of  9's  in  the  entire  number. 

PKOPERTipS   OF   11 

89.  Any  number  of  lO's  is  equal  to  the  same  number  of  ll's 
minus  the  same  number  of  units;  any  number  of  lOO's  is  equal 
to  the  same  number  of  99's  plus  the  same  number  of  units ;  any 
number  of  lOOO's  is  equal  to  the  same  number  of  lOOl's  minus 
the  same  number  of  units ;  and  so  on. 

Thus,  40  =  four  ll's  -  4;  500  =  five  99's  +  5;  7000  =  seven  lOOl's -  7. 

90.  It  is  therefore  clear  that  even  powers  of  10  are  multiples 
of  11  plus  1  and  odd  powers  of  10  are  multiples  of  11  minus  1. 

Thus,  102  or  100  =  nine  ll's  +  1 ;  10^  or  1000  =  ninety-one  ll's  -  1 ;  10* 
or  10,000  =  nine  hundred  nine  ll's+  1. 

91.  From  the  foregoing  it  is  evident  that: 

The  excess  of  Ifs  in  any  number  is  equal  to  the  sum  of  the  digits 
in  the  odd  places  (increased  by  11  or  a  multiple  of  11  if  necessary^ 
minus  the  sum  of  the  digits  in  the  even  places. 

Thus,  the  excess  of  ll's  in  45  is  1  (5  —  4)  ;  the  excess  of  ll's  in  125  is 
4  (5^^  +  r=^) ;  the  excess  of  ll's  in  2473  is  9  (3  +  4  +  11  -  7T2  =  9)  j 
the  excess  of  Xl's  in  14,206  is  5. 


CHECKING  RESULTS  73 

Checking  Addition  and  Subtraction 

92.    Examples,     i.    By   casting  out    the    9's,  show  that  the 
sum  of  935,  651,  782,  and  465  is  2833. 

Solution.  The  sum  of  the  digits  in  935  is  17  ;  but  since  17  935  =  8 
contains  9,  find  the  sum  of  the  digits  in  17  and  the  result,  8,  is  the  (?ci  _  o 
excess  of  9's  in  the  entire  number.  In  like  manner  find  the  ex- 
cess  of  9's  in  651,  782,  and  465.  Since  935  is  a  multiple  of  9  +  8,  *  °^  ~  ^ 
651  a  multiple  of  9  +  3,  782  a  multiple  of  9  +  8,  465  a  multiple  of  465  =  6 
9  +  6,  the  sum  of  these  numbers,  2833,  should  equal  a  multiple  of  2833  =  7 
9  +  (8  +  3  +  8  +  6),  or  9  +  25.  25  is  a  multiple  of  9  +  7,  and  2833 
is  a  multiple  of  9  +7  ;  hence,  the  addition  is  probably  correct. 

2.    By  casting  out  the  ll's,  show  that  the  sum  of  648,  217, 
451,  and  688  is  2004. 


Solution.     8-4  +  6-0  =  10,   the  excess  of    ll's    in  648.  648=10 

7-1+2  -0=8,  the  excess  of  ll's  in  217.     12  (11+1) -5+  917=    8 

4  —  0  =  11;  but  11  contains  11,  hence,  the  excess  of  ll's  in  451 

is  0.    8  -  8  +  6  -  0  =  6,  the  excess  of  ll's  in  688.     Since  648  is  451=    0 

a  multiple  of  11  +  10,  217  a  multiple  of  11  +  8,  451  a  multiple  of  688=    6 

11,  and  688  a  multiple  of  11  +  6,  the  sum  of  these  numbers,  2004,  2004  =    2 

should  be  a  multiple  of  11  +  (10  +  8+  6),  or  11  +  24.     24  is  a 

multiple  of  11  +  2  and  2004  is  a  multiple  of  11  +  2;  hence,  the  addition  is 

probably  correct. 

93.  Subtraction  may  be  proved  either  by  casting  out  the  9's 
or  ll's  in  practically  the  same  manner  as  addition. 

The  difference  between  the  excess  of  9's  or  ll's  in  the  minuend  and  sub- 
trahend should  equal  the  excess  of  9's  or  ll's  in  the  remainder;  or  the  sum 
of  the  excess  of  9's  or  ll's  in  the  subtrahend  and  remainder  should  equal 
the  excess  of  9's  or  ll's  in  the  minuend. 

These  methods  are  but  little  used  for  checking  addition  and  subtraction. 
Addition  is  generally  checked  as  explained  on  page  12,  and  subtraction  as 
explained  on  page  24.  On  the  other  hand,  long  multiplications  and  divi- 
sions are  almost  always  checked  by  applying  the  properties  of  9  or  11. 

Checking  Multiplication  and  Division 

94.  Examples,  i.  By  casting  out  the  9's  show  that  the 
product  of  64  x  95  is  6080. 

Solution.    The  excess  of  9's  in  95  is  5,  and  in  64,  1.    Since  95  qc  _  c 

is  a  multiple  of  9  +  5  and  64  a  multiple  of  9  +  1,  the  product  of  />  <  ~~  i 

64  X  95  should  be  a  multiple  of  9  plus  (1x6).    1  x  5  or  5  equals  ^^  ~  i 

the  excess  of  9's  in  6080  ;  hence,  the  work  is  probably  correct.  6080  =  6 


74  CONCISE   BUSINESS   ARITHMETIC 

2.  By  casting  out  the  ll's  show  that  the  product  of  46  x  95 
is  4370. 

SomxioN.    The  excess  of  ll's  in  95  is  7,  and  in  46,  2.     Since  95  —  7 

95  is  a  multiple  of  11  +  7  and  46  a  multiple  of  11  +  2,  the  prod-  4fi  —  9 

uct  of  46  X  95  should  be  a  multiple  of  11  plus  (2  x  7)  or  14 ;  but  ~~  - 

14  is  a  multiple  of  11  +  3.     Since  the  product  4370  is  a  multiple  of  4370  =  3 
11  +  3,  the  work  is  probably  correct. 

95.  Division  may  be  proved  either  by  casting  out  the  9's  or 
ll's  in  practically  the  same  manner  as  multiplication.  The 
excess  of  9's  or  ll's  in  the  quotient  multiplied  by  the  excess 
of  9's  or  ll's  in  the  divisor  should  equal  the  excess  of  9's  or 
ll's  in  the  dividend,  minus  the  excess  of  9's  or  ll's  in  the  re- 
mainder, if  any. 

Casting  out  the  9's  will  not  show  an  error  caused  by  a  transposition  of 
figures;  but  casting  out  the  ll's  will  show  such  an  error.  The  method  of 
casting  out  the  ll's  is  therefore  considered  the  better  proof. 

WRITTEN  EXERCISE 

1.  Determine  without  dividing  whether  $2.64  is  the  quo- 
tient of  $1375.44-- 521. 

2.  X)etermine  without  multiplying  whether  $1807.50  is  the 
product  of  482  times  $3.75. 

3.  Determine  without  adding  whether  4231  is  the  sum  of 
296,  348,  924,  862,  956,  and  845. 

4.  Multiply  34,125  by  729  in  two  lines  of  partial  products 
and  verify  the  work  by  casting  out  the  9's. 

5.  Find  the  cost  of  173,000  shingles  at  $4.27  per  thousand, 
in  two  lines  of  partial  products,  and  verify  the  work  by  casting 
out  the  ll's. 

6.  Find  the  cost  of  126,000  ft.  of  clear  pine  at  $24.60  per 
thousand,  in  two  lines  of  partial  products,  and  verify  the  work 
by  casting  out  the  9's. 

7.  Find  the  cost  of  2,191,000  ft.  of  flooring  at  $32.08  per 
thousand,  in  two  lines  of  partial  products,  and  verify  the  work 
by  casting  out  the  ll's. 


FRACTIONS 


CHAPTER   VII 


DECIMAL  FRACTIONS 


ORAL  EXERCISE 

1.  In  the  number  $7.62  what  figure  stands  for  the  dollars? 
the  tenths  of  a  dollar?  the  hundredths  of  a  dollar? 

2.  What  name  is  given  to  the  point  which  separates  the 
whole  number  of  dollars  from  the  part  of  a  dollar  ? 

3.  Read:  3.5  dollars;  3.5  ft.;  27.5  1b.;  .7  of  a  dollar;  .5 
of  a  ton;  16.6;  .9;  9.25  dollars;  7.25ft.;  8.75  rd.;  .95  of  a 
dollar;  .85  of  a  pound  sterling  ;   .57. 

4.  What  is  the  first  place  at  the  right  of  the  decimal  point 
called  ?  the  second  place  ? 

5.  In    the    accompanying      S) 
diagram  what  part  of  J.  is  ^  ? 
What  part  of  jB  is  (7?    What 
part  of  G  is  D? 

6.  What  part  of  A  is  (7? 
What  part  of  ^  is  D?  b  a 

7.  If  ^  is  a  cubic  inch,  what  is  ^?   (7?  D? 

8.  In  a  pile  of  10,000  bricks  one  brick  is  what  part  of  the 
whole  pile?  10  bricks  is  what  part  of  the  whole  pile?  100 
bricks  is  what  part  of  the  whole  pile?  1000  bricks  is  what 
part  of  the  whole  pile  ? 

9.  How  may  one  tenth  be  written  besides  y^^?  one  hun- 
dredth besides  -^-^  ?  one  thousandth  besides  y^^'^  ^ 

96.  Units  expressed  by  figures  at  the  right  of  the  decimal 
point  are  called  decimal  units. 

97.  A  number  containing  one  or  more  decimal  units  is 
called  a  decimal  fraction  or  a  decimal. 


CB 


76 


76  COKCISE   BUSIKESS   ARITHMETIC 

NOTATION  AND  NUMERATION 

ORAL  EXERCISE 

1.  Read:  0.7;  0.03  ;  0.25.  How  many  places  must  be  used 
to  express  completely  any  number  of  hundredths? 

2.  Read:  0.004;  0.025;  0.725.  How  many  places  must  be 
used  to  express  completely  any  number  of  thousandths  ? 

3.  Read:  .0005;  .00007;  .000009;  .0037;  .00045;  .000051; 
.0121;    .00376;    .000218;    .1127;    .01525;    .004531;    .16067. 

4.  How  many  places  must  be  used  to  express  completely  any 
number  of  ten-thousandths?  any  number  of  hundred-thou- 
sandths ?  any  number  of  millionths  ? 

98.  In  reading  decimals  pronounce  the  word  and  at  the 
decimal  point  and  omit  it  in  all  other  places. 

Thus,  in  reading  0.605  or  .605  say  sia:  hundred  Jive  thousandths;  in  reading 
600.005  say  six  hundred  and  Jive  thousandths. 

99.  'The  relation  of  integers  and  decimals  with  their  increas- 
ing and  decreasing  orders  to  the  left  and  to  the  right  of  the 
decimal  point  is  shown  in  the  following 

Numeration  Table 


Periods  : 

Millions 

Thousands 

Units 

Thousandths 

Millionths 

"• 

f 

' 

"  "* 

^ 

' 

OQ 

CO 

tS 

Ti 

80 

Orders :     ^ 

i 

05 

1 

1 

1 

a 

09 

-a 

« 

i 

s  1 

1 

73 

CO 

0 

1 

1 

if 

W 

1 

>? 

a 

1 

1 

g 

ii 

e 

1 

11 

9 

8 

7, 

6 

5 

4, 

3 

2 

1 

.    2 

3 

4 

5 

6    7 

100.  Hundredths  are  frequently  referred  to  as  per  cent,  a 
phrase  originally  meaning  hy  the  hundred, 

101.  The  symbol  %  stands  for  hundredths  and  is  read  j^^r  cent. 
Thus  45%  =  .45 ;  48%  of  a  number  =  .48  of  it. 


DECIMAL  FRACTIONS  77 

ORAL  EXERCISE 

Read  : 

1.  0.073.  5.  532.002.  9.  31.08%. 

2.  0.00073.  6.  60.0625.  lo.  126.75%. 

3.  3004.025.  7.  63.3125.  li.  2150.1875. 

4.  300.4025.  8.  126.8125.  12.  3165.00625. 

13.  131.3125  T.  15.   A  tax  of  1.0625  mills. 

14.  240.0125  A.  16.  A  tax  of  9.1875  mills. 

17.  Read  the  number  in  the  foregoing  numeration  table. 

18.  Read  the  following,  using  the  words  "  per  cent " :  .17; 
28;   .85;  .67;  .425;  .371. 

19.  Read  the  following  as  decimals,  not  using  the  words 
"percent":  25%;  75%;   87%;    621%;  27.15%. 

20.  Read  aloud  the  following  : 

a.  The  value  of  a  pound  sterling  in  United  States  money  is 
$4.8665. 

h.  A  meter  (metric  system  of  measures)  is  equal  to 
39.37079  in.;  a  kilometer,  to  0.62137  mi. 

c.  1  metric  ton  is  equal  to  1.1023  ordinary  tons;  1.5  metric 
tons  are  equal  to  1.65345  ordinary  tons. 

d.  A  flat  steel  bar  3  in.  wide  and  0.5  in.  thick  weighs 
5.118  lb. 

e.  The  circumference  of  a  circle  is  3.14159  times  the  length 
of  its  diameter. 

WRITTEN  EXERCISE 

Write  decimally  : 

1.  Five  tenths ;  fifty  hundredths ;  five  hundred  thousandths. 

2.  Nine  hundred  and  eleven  ten-thousandths ;  nine  hundred 
eleven  ten-thousandths ;    five  hundred  and  two  thousandths. 

3.  One  hundred  seventy-four  millionths;  one  hundred 
seventy-four  million  and  seven  millionths;  seven  million  and 
one  hundred  seventy-four  millionths. 

4.  Seven  thousand  and  seventy-five  ten-thousandths;  two 
hundred  fifty-seven  ten-millionths ;  two  hundred  and  forty-six 
millionths ;  two  hundred  forty-six  millionths. 


78  CONCISE   BUSINESS   ARITHMETIC 

5.  Four  million  ten  thousand  ninety-seven  ten-millionths ; 
four  million  ten  thousand  and  ninety-seven  ten-millionths;  five 
hundred  millionths ;  five  hundred-millionths. 

6.  Six  hundred  six  and  five  thousand  one  hundred-thou- 
sandths; six  hundred  six  and  fifty-one  hundred-thousandths; 
fifty-six  and  one  hundred  twenty-eight  ten-billionths. 

7.  Seventeen  thousand  and  eighteen  hundred  seventy-six 
millionths ;  seventeen  thousand  and  eighteen  hundred  seventy- 
six  ten-thousandths ;  twenty-one  hundred  sixteen  hundredths. 

102.  In  the  number  2.57  there  are  2  integral  units,  5  tenths 
of  a  unit,  and  7  hundredths  of  a  unit.  In  the  number  2.5700 
there  are  2  integral  units,  5  tenths  of  a  unit,  7  hundredths  of 
a  unit,  0  thousandths  of  a  unit,  and  0  ten-thousandths  of  a  unit. 
2.5700  is  therefore  equal  to  2.57.     That  is, 

Decimal  ciphers  may  he  annexed  to  or  omitted  from  the  right 
of  any  number  without  changing  its  value, 

ORAL  EXERCISE 

Read  the  following  (a)  as  printed  and  (5)  in  their  simplest 
decimal  form : 

1.  0.700.  3.    16.010.  5.    0.50.  7.    0.7000. 

2.  5.2450.        4.    18.210.  6.    0.00950.  8.    12.9010. 

ADDITION 

ORAL  EXERCISE 

1.    What  is  the  sum  of  0.4,  0.05,  0.0065  ? 
,    2.    What  is  the  sum  of  0.3,  0.021,  0.008  ? 

3.  Find  the  sum  of  seven  tenths,  forty-four  hundredths,  and 
two;  of  four  tenths,  twenty-one  hundredths,  and  six  thou- 
sandths. 

103.  Example.    Find  the  sum  of  12.021,  256.12,  and  27.5. 

Solution.    Write  the  numbers  so  that  their  decimal  points  12.021 

stand  in  the  same  vertical  column.    Units  then  come  under  units,  256  12 
tenths  under  tenths,  and  so  on.    Add  as  in  integral  numbers  and  ^„  - 

place  the  decimal  point  in  the  sum  directly  under  the  decimal  '. 

points  in  the  several  numbers  added.  295.641 


DECIMAL   FRACTIONS  79 

WRITTEN   EXERCISE 
Find  the  sum  of: 

1.  7.5,  165.83,  5.127,  6.0015,  and  71.215. 

2.  257.15,  27.132,  5163,  8.000125,  and  4100.002. 

3.  0.175,  5.0031,  .00127,  70.2116001,  and  21.00725. 

4.  51.6275,  19.071,  0.000075,  21.00167,  and  40,000.01. 

5.  2.02157,  2.1785,  2500.00025,  157.2165,  and  7.0021728. 

6.  Copy,  find  the  totals  as  indicated,  and  check : 

$1241.50  $9215.45  $1421.12  $1421.32  ?* 

1.52  1275.92  1.46  1618.40  ? 

349.21  3725.41  2.18  1920.41  ? 

2975.47  7286.95  7.96  10.20  ? 

27.14  8276.92  14.21  41.64  ? 

9218.49  7271.44  1240.80  126.18  ? 

5.17  8926.95  7216.80  24.17  ? 

12627.85  8972.76  4.75  240.20  ? 

721.92  7214.25  8.16  960.80  ? 

11.41  8142.76  .47  1860.45  ? 

1.21  8436.14  .92  9270.54  ? 

.72  8435.96  9.26  75.86  ? 

14178.21  7926.11  1490.75  45.95  ? 

2172.14  9214.72  1860.54  75.86  ? 

726.95  1241.16  9265.80  72.18  ? 

85.21  4214.71  625.50  9260.14  ? 

75.92  8726.19  240.75  1.20  ? 

72604.25  2140.12  60.50  7.40  ? 

124.61  7146.14  120.41  8.32  ? 

2114.62  7214.86  4101.08  2860.14  I 

?         ?  ?  ?  ? 

7.  Find  the  sum  of  twenty-one  hundred  sixty-five  and  one 
hundred  sixty-five  ten-thousandths,  thirty-nine  and  twelve 
hundred  sixty-five  millionths,  twenty-seven  hundred  thirty- 
six  and  one  millionth,  four  and  six  tenths,  six  hundred  and 
six  thousandths,  and  six  hundred  sixty-five  thousandths. 


80  CONCISE   BUSINESS   ARITHMETIC 

SUBTRACTION 

ORAL  EXERCISE 

1.  From  the  sum  of  0.7  and  0.4  take  0.5. 

2.  From  the  sum  of  0.07  and  0.21  take  0.006. 

3.  From  seventy-four  hundredths  take  six  thousandths. 

4.  To  the  difference  between  .43  and  .03  add  the  sum  of 
.45  and  .007. 

5.  Goods  on  hand  at  the  beginning  of  a  week,  $24.50; 
goods  purchased  during  the  week,  $35.50;  goods  sold  during 
the  week,  $36 ;  goods  on  hand  at  the  close  of  the  week,  $36.50. 
What  was  the  gain  or  loss  for  the  week  ? 

104.   Example.     From  14.27  take  5.123. 

Solution.     Write  the  numbers  so  that  the  decimal  points  stand         14. 27 
in  the  same  vertical  column.    The  minuend  has  not  as  many  places  ^  1 9Q 

as  the  subtrahend  ;  hence  suppose  decimal  orders  to  be  annexed  ' 

until  the  right-hand  figure  is  of  the  same  order,  then  subtract  as  o.L^i 

in  integers  and  place  the  decimal  point  in  the  remainder  directly  under  the 
decimal  points  in  the  numbers  subtracted. 


WRITTEN  EXERCISE 

Find  the  difference  between^ 

1.  7.2154  and  2.8576.  5.    9  and  5.2675. 

2.  17.2157  and  1.0002.  6.    16  and  5.0000271. 

3.  1.0005  and  .889755.  7.    .0002  and  .000004. 

4.  $1265.45  and  $87.99.  8.    24.503  and  17.00021. 
9.    The  sum  of  two  numbers  is  166.214.     If  one  of  the 

numbers  is  40.21,  what  is  the  difference  between  the  numbers? 

10.  The  minuend  is  127.006  and  the  remainder  15.494. 
What  is  the, sum  of  the  minuend,  subtrahend,  and  remainder? 

11.  From  the  sum  of  ninety-nine  ten-thousandths,  one  hun- 
dred fifty-one  and  five  thousandths,  two  hundred  fifty -two  and 
twenty -five  millionths,  six  tenths,  and  eighteen  and  one  hun- 
dred seventy-five  thousandths  take  the  sum  of  twelve  hundred 
fifteen  millionths,  and  one  hundred  eighty-eight  thousandths. 


DECIMAL  FRACTIONS  81 

12.  From  the  sum  of  two  hundred  fifty-seven  thousandths 
and  eight  and  one  hundred  twenty -six  millionths  take  the  sum 
of  live  hundred  ten  thousandths  and  two  and  one  hundred 
twenty-four  ten-thousandths. 

13.  A  merchant  had,  at  the  beginning  of  a  year,  goods 
amounting  to  §8165.95.  During  the  year  his  purchases 
amounted  to  §5265.90  and  his  sales  to  $9157.65.  At  the  close 
of  the  year  he  took  an  account  of  stock  and  found  that  the 
goods  on  hand  were  worth  §7216.56.  What  was  his  gain  or 
loss  for  the  year? 

14.  A  provision  dealer  had  on  hand  Jan.  1,  goods  worth 
§4127.60.  His  purchases  for  the  year  amounted  to  §4165.95 
and  his  sales  to  §6256.48.  Dec.  31  of  the  same  year  his  in- 
ventory showed  that  the  goods  on  hand  were  worth  §3972.50. 
If  the  amount  paid  for  freight  on  the  goods  bought  amounted 
to  §237.50,  what  was  his  gain  or  loss  on  provisions? 

15.  I  had  on  hand  Jan.  1,  lumber  amounting  to  §4210.60. 
During  the  year  my  purchases  amounted  to  §3126.50,  and  my 
sales  to  §4165.85.  I  lost  by  fire  lumber  valued  at  §506.75,  for 
which  I  received  from  an  insurance  company  §500.  Dec. 
31,  my  inventory  showed  the  lumber  to  be  worth  §5209.08. 
How  much  did  I  gain  or  lose  on  lumber  during  the  year? 

16.  At  the  beginning  of  a  year  my  resources  were  as  follows: 
cash  on  hand,  §1262.50;  goods  in  stock,  §1742.85;  account 
against  A.  M.  Eaton,  §146.50.  At  the  same  time  my  liabili- 
ties were  as  follows:  note  outstanding,  §156.85;  account  in 
favor  of  Robert  Wilson,  §521.22.  During  the  year  I  made  an 
additional  investment  of  §1250.65,  and  withdrew  for  private 
use  §275.  I  sold  for  cash  during  the  year  goods  amounting  to 
§1250.75,  and  bought  for  cash  goods  amounting  to  §530.90  ;  I 
also  paid  Robert  Wilson  §320  to  apply  on  account.  At  the 
close  of  the  year  my  inventory  showed  goods  in  stock  valued  at 
§750.48.  What  was  my  gain  or  loss  for  the  year  and  my  pres- 
ent worth  at  the  close  of  the  year  ? 

Do  not  fail  to  check  all  problems.  No  phase  of  arithmetic  is  more 
important. 


82  CONCISE   BUSINESS   ARITHMETIC 

MULTIPLICATION 

ORAL  EXERCISE 

1.  How  many  times  .4  is  4  ?  .77  is  7.7  ?  .999  is  9.99? 

2.  44  is  how  many  times  .44?  22  is  how  many  times  .022? 
1  is  how  many  times  .001  ?  .01  is  how  many  times  .0001  ? 

3.  Read  aloud  the  following,  supplying  the  missing  terms : 
Removing  the  decimal  point   one   place   to   the   right   multi- 
plies  the  value  of  the  decimal  by ;  two  places, the 

value  by ;  three  places, the  value  by  . 

4.  Multiply  12.1252  by  1000  ;  by  100  ;  by  100,000. 

5.  Multiply  89.375  by  100;  by  10,000  ;  by  100,000. 

6.  Multiply  5.15  by  10;  by  100;  by  1000;  by  10,000. 

7.  Multiply  .000016  by  1000;  by  100,000;  by  1,000,000. 

8.  Multiply  167.50  by  10  ;  by  100  ;  by  1000  ;  by  10,000. 

9.  Multiply  .0037  by  10;  by  100;  by  1000;  by  10,000,000. 

10.  What  part  of  1  is  .1  ?  of  7  is  .7?  of  29  is  2.9? 

11.  What  part  of  84  is  .84?  of  129  is  1.29?  of  1275  is  12.75? 

12.  What  part  of  .6  is  .006  ?  of  .64  is  .0064? 

Read  aloud  the  following,  supplying  the  missing  terms : 
a.  Each  removal  of  the  decimal  point  one  place  to  the  left 
the  value  of  the  decimal  by  10. 


h.    To  divide  a  decimal  by is  to  find  one  tenth  (.1)  of 

it,  or  to it  by  .1. 

13.  Give  a  short  method  for  multiplying  a  number  by  .1 ;  by 
.01 ;  by  .001 ;  by  .0001. 

14.  Multiply  .009  by  .1;  by  .01;  by  .001. 

15.  Multiply  217.59  by  .1;  by  .01;  by  .001. 

16.  Multiply  54.65  by  .01;  by  .00001;  by  .000001. 

17.  Multiply  2.375  by  .1;  by  .01;  by  .001 ;  by  .0001. 

18.  Multiply  25.215  by  .1;  by  .01;  by  .001;  by  .0001. 

19.  Multiply  2111  by  .01 ;  by  .001 ;  by  .0001 ;  by  .00001. 

20.  Compare   2400x80.06   with   100x24x80.06  or  with 
24  X  ^Q. 

21.  Compare  3000  x  612.251  with  1000  x  3  x  612.251,  or  with 
3  X  612251. 


DECIMAL  FRACTIONS  83 

22.  Multiply  21.25  by  2400. 

Solution.    2400  is  24  times  100.     Multiply  by  100  2125  2125 

by  removing  the  decimal  point  two  places  to  the  right.  oj.  24 

The  result  is  2125.     24  times  2125  equals  51,000,  the  ■    -^^  TKFTT 

required  product.  ^^^^  ^250 

In  multiplying  begin  with  either  the  lowest  or  the  4250  8500 

highest  digit  in  the  multiplier  as  shown  in  the  margin.  51000  51000 

23.  Formulate  a  brief  rule  for  multiplyiug  a  decimal  by  any 
number  of  lO's,  lOO's,  lOOO's,  etc. 

24.  Find  the  cost  of  : 

a,  500  lb.  at  18^.  d,  600  lb.  at  29)^.  g,  900  lb.  at  34^. 
h,  150  lb.  at  14^.  e,  300  lb.  at  41^.  h,  700  lb.  at  51^. 
c.    200  lb.  at  26/^.      /.    400  lb.  at  121^.    i.    1400  lb.  at  5^. 

105.   Examples,     l.   Multiply  41.127  by  4. 

Solution.  41.127  is  equal  to  41,127  thousandths.  41,127  thou-  41.127 
sandths  multiplied  by  4  equals  164,508  thousandths,  or  164.508.     That  4 

is,  thousandths  multiplied  by  a  whole  number  must  equal  thousandths.    164.508 

2.    Multiply  41.127  by  .04. 

Solution.     The  multiplier,  .04,  is  equal  to  4  times,  01 ;  therefore,  41.127 

multiply  by  4  and  by  .01.    Multiplying  by  4,  as  in  problem  1,  the  q^ 

result  is  164,508.     Multiplying  by  .01,  by  simply  moving  the  decimal  i  nA  g rtQ 

point  in  the  product  two  places  to  the  left,  the  result  is  1.64508.  -L.O^OUo 

It  will  be  seen  that  the  number  of  decimal  places  in  the  product 
is  equal  to  the  decimal  places  in  the  multiplicand  and  multiplier. 

It  should  not  be  necessary  to  memorize  the  above  rule.  The  student 
should  know  at  a  glance  that  the  product  of  tenths  and  tenths  is  hundredths, 
of  tenths  and  hundredths  is  thousandths,  and  so  on. 

ORAL   EXERCISE 

1.  In  multiplying  24.05  by  3.14  can  you  tell  before  multiply- 
ing how  many  integral  places  there  will  be  in  the  product  ? 
how  many  decimal  places  ?     Explain. 

2.  How  many  integral  places  will  there  be  in  each  of  the  fol- 
lowing products  :  2.5x4.015?  27.51x3.1416?  321.1  x 
201.51?  1.421x42.267?  126.5  x  .01?  1020x5.01?  .105x6? 
2.41  X  10.05  ?  How  many  decimal  places  will  there  be  in  each 
of  the  above  products  ? 


84 


CONCISE   BUSINESS  ARITHMETIC 


3.  What  are  400  bbl.  of  apples  worth  at  $2.12  per  barrel? 
at  il.27l  per  barrel? 

4.  I  bought  60  lb.  of  sugar  at  $0,041  and  gave  in  payment  a 
five-dollar  bill.     How  much  change  should  I  receive? 

5.  A  and  B  are  partners  in  a  manufacturing  business,  A  re- 
ceiving 52  %  and  B  48  %  of  the  yearly  profits.  The  profits  for 
a  certain  year  are  $5000.  Of  this  sum  how  much  should  A  and 
B,  respectively,  receive  ? 

WRITTEN  EXERCISES 

Find  the  product  of : 

1.  3.121  X  152.           4.  12.14  X  265.  7.  2.531  x  31000. 

2.  3121  X  .152.           5.  9.004  x  .021.  8.  .1724  x  18000. 

3.  31.21  X  15.2.          6.  .3121  X  .0152.  9.  .15539  x  2002. 

10.  A  man  owned  75%  of  a  gold  mine  and  sold  50%  of  his 
share.  What  is  the  remainder  worth  if  the  value  of  the  whole 
mine  is  $425,000? 

11.  A  man  bought  a  farm  of  240  A.  at  $137.50  per  acre. 
He  sold  75%  of  it  at  $150  per  acre,  and  the  remainder  at  $175 
per  acre.     What  was  his  gain  ? 

12.  Copy  and  complete  the  following  table  of  statistics. 
Check  the  results.  (The  total  yield  multiplied  by  the  price 
per  bushel  should  equal  the  total  valuation.) 

Largest  "Wheat-growing  States  in  a  Recent  Year 


State 

Yield  in  Bushels 

Farm  Price 
PER  Bushel 

Farm  Valuation 

North  Dakota 
Kansas 
Minnesota 
South  Dakota 

143,820,000 
92,290,000 
67,038,000 
52,185,000 

92.4^ 

92  A  f 
92  A  f 
92  A  ^ 

? 
? 
? 
? 

Total 

? 

? 

? 

13-15.    Make  and  solve  three  self-checking  problems  in  multi- 
plication of  decimals. 


DECIMAL  FRACTIONS  85 

DIVISION 

ORAL  EXERCISE 

1.  Divide  by  8:  64  ft.,  .64,  .064,  6.4. 

2.  Divide  by  9 :  63  in.,  .63,  .063,  6.3. 

3.  Divide  by  16:  |640,  $6.40,  6.4,  .64,  .064. 

4.  Divide  by  15:  $15.75,  $7.50,  $0.75,  30.45,  3.045,  .3045. 

5.  Divide  337.5  by  45. 

7^ 

45)337.5 

315     =  45  times  7 
22.5  undivided 
22.5  =45  times  .5 

Check.    45  times  7.5  =  337.5 ;  hence,  the  work  is  correct 

106.  In  the  above  exercise  it  is  clear  that  when  the  divisor  is 
an  integer,  each  quotient  figure  is  of  the  same  order  of  units  as  the 
right-hand  figure  of  the  partial  dividend  used  to  obtain  it. 

ORAL  EXERCISE 

1.  500  is  how  many  times  50?  $75  is  how  many  times 
$7.50? 

2.  Divide  50  by  5 ;  500  by  50.  How  do  the  quotients 
compare  ? 

3.  Divide  7.50  by  15  ;  $75  by  150.  How  do  the  quotients 
compare  ? 

4.  720  is  how  many  times  72  ?     9  is  how  many  times  .9? 

5.  Divide  720  by  9;  72  by  .9;  7.2  by  .09;   .72  by  .009. 

107.  It  has  been  seen  that  multiplying  both  dividend  and 
divisor  by  the  same  number  does  not  change  the  quotient. 

108.  Therefore,  to  divide  decimals  when  the  divisor  is  not  an 

integer : 

Multiply  both  dividend  and  divisor  by  the  power  of  10  that 
will  make  the  divisor  an  integer^  and  divide  a%  in  United  States 
money. 


86 


CONCISE   BUSINESS   ARITHMETIC 


109.    Divide  0.3375  by  0.45. 
.3375  ^  .45  =  33.75  --  45.     33.75  -^  45  =  .7,  with  a  remainder  of 
2.25.     2.25  -J-  45  =  .05.     The  quotient  is  therefore  .75.  45TsTT^ 

Observe  that  the  divisor  may  always  be  made  an  integer  if  the  ^1  \ 

decimal  point  in  the  dividend  is  carried  to  the  right  as  many  places 
as  there  are  decimal  places  in  the  divisor. 

Should  there  be  a  remainder  after  using  all  the  decimal 


75 


2  25 

2  25 


places  in  the  dividend,  annex  decimal  ciphers  and  continue  the  division 
as  far  as  is  desired. 

ORAL   EXERCISE 


Divide  : 

1.  Ibyl. 

19. 

33  by  .11. 

2.  Iby.l. 

20. 

33  by  110. 

3.  IbylO. 

21. 

.33  by  .11. 

4.  .Iby.l. 

22. 

3.3  by  1.1. 

5.  1  by  .01. 

23. 

.0001  by  1. 

6.  1  by  100. 

24. 

33  by  .011. 

7.  1  by  .001. 

25. 

33  by  1100. 

8.  .10  by  .10. 

26. 

.0001  by  .1. 

9.  .01  by  .01. 

27. 

3300  by  .11. 

10.  1  by  1000. 

28. 

330  by  .011. 

11.  1  by  .0001. 

29. 

33  by  .0011. 

12.  1  by  10,000. 

30. 

33  by  11000. 

13.  1  by  .00001. 

31. 

.0001  by  .01. 

14.  .001  by  .001. 

32. 

.033  by  .011. 

15.  1  by  100,000. 

33. 

.0001  by  .001. 

16.  1  by  .000001. 

34. 

.0033  by  .0011. 

17.  .0001  by  .0001. 

35. 

.0001  by  .0001. 

18.  .00001  by  .00001. 

36. 

.0001  by  .00001. 

WRITTEN  EXERCISE 

Divide : 

1. 

5842  by  .046.   6.  2200  by  .44. 

11.  16  by  .0064. 

2. 

2.592  by  .108.  7.  231.6  by  579. 

12.  1.86  by  31,000. 

3. 

1.750  by  8750.  8.  950  by  19,000. 

13.  1600  by  64,000. 

4. 

.00338  by  .013.  9.  81.972  by  .00009. 

14.  .0004  by  20,000. 

5.    1.728  by  .0024.  10.  115.814  by  .00079.   15.    100  by  .000001. 


L>EC1MAL  FKACTIONS 


87 


Find  the  sum 

of  the  quotients  : 

16. 

17. 

18. 

8.1-^.9. 

72-^8. 

125^250. 

81-f-.09. 

72 -.8. 

12.5-2.5. 

8.1 -.09. 

7.2 -.8. 

1.25^2.5. 

.81 -V- 900. 

72 -.08. 

12.5^250. 

.0081-9. 

.72 -.08. 

125  ^  2500. 

8.1^900. 

72 --.008. 

.125^.025. 

810 -.009. 

72-8000. 

12500 -.25. 

.0081^9000. 

72-^.0008. 

125-^25000. 

81000 -.009. 

.072 -f- .008. 

12500 -.025. 

81-^.000009. 

72 -J-.  00008. 

125  ^  250000. 

8100  -  90000. 

.0072-^.0008. 

.125 -f-. 00025. 

.00081-5-90000. 

.00072 -f- .00008. 

12500  ^  .0025. 

19. 

20. 

21. 

8.8-4-2.2. 

17^68. 

36^.072. 

.88 -5- .22. 

1.7 -f- 6.8. 

3.6^.072. 

88 -f-.  0022. 

.17-^.68. 

.36^.072. 

8.8 -i- 2200. 

1.7-^680. 

360^.072. 

880-^2200. 

170^680. 

.036  H-  .072. 

8.8-^2.200. 

.017^.068. 

'  3.6^72000. 

880^.2200. 

1.7-^68000. 

36  ^  720000. 

8800  -f-  2200. 

1700  --  6800. 

360 -.00072. 

880-^22000., 

1700  -  68000. 

3600 --.0072. 

880-^.0002^ 

.0017^.0068. 

.0036^.0072. 

88000-^.0022. 

.00017^.00068. 

3.6^.000072. 

88000 -J-.  00022. 

.000017^.000068. 

.00036^.00072. 

22.    The  proc 

luct  of  two  numbers  is  0.00025.     If  one  of  the 

numbers  is  0.0025,  what  is  the  other? 

23.  A  retailer  bought  450  yd.  of  cloth  for  $1237.50  and 
sold  it  at  $3.25  per  yard.     How  much  did  he  gain  per  yard? 

24.  A  drover  bought  a  flock  of  sheep  at  the  rate  of  $3.30 
per  head.  He  sold  them  at  a  profit  of  $0.20  per  head  and 
received  $700.  How  many  sheep  were  there  in  the  flock 
and  what  was  his  gain? 


88 


CONCISE   BUSINESS   ARITHMETIC 


25.    Copy   and  complete  the   following   table.      Check   the 
results. 


Largest  Oat-growing  States  in  a  Recent  Year 

State 

Yield  in  Bushels 

Farm  Price 
PER  Bushel 

Farm  Valuation 

Illinois 
Iowa 

Wisconsin 
Minnesota 

? 
? 
? 
? 

31^ 
31^ 
31^ 
31^ 

54,818,000 
58,811,000 
27,119,000 
31,926,000 

Total 

? 

31^ 

? 

26-28.    Make    and    solve    three    self -checking    problems   in 
division   of  decimals. 

DIVIDING   BY  POWERS   AND   MULTIPLES   OE  TEN 

ORAL  EXERCISE 

1.  6.4  is  what  part  of  64?     $0.17  is  what  part  of  $1.70  ? 

2.  Compare  (as  in  problem  1)  $240.60  with  $24,060;  17.75 
ft.  with  1775  ft. 

3.  Compare  (as  in  problem  1)  .1  with  1;   .01  with  1;   .001 
withl;  .0001  with  1. 

4.  Read  aloud  the  following,  supplying  the  missing  terms : 

Removing  the    decimal  place   to   the   divides   the 

value  of  the  decimal  by  10  ;  two  places, the  value  of  the 

decimal  by  ;  three  places, the  value  of '  the  decimal 

by . 

5.  Compare  the  quotient  of    28  -j-  .7  with  the  quotient   of 

.7  with  the  quotient  of 


28  X  10  -f-  .7  X  10  ;  the  quotient  of  28 
280  -^  7. 

6.  Compare  the  quotient  of  16.4-5-40  with  the  quotient  of 
16.4  -5- 10  -7-40-^10;  the  quotient  of  16.4  ^  40  with  the  quotient 
of  1.64  -f-  4.     What  is  the  quotient  of  56.77  divided  by  7000? 


.00811 


Solution.    Eemoving  the  decimal  point  three  places  to  the 

left  and  dropping  the  ciphers  of  the  divisor  is  equivalent  to  dividing         

both  dividend  and  divisor  by  1000  and  does  not  change  the  value     7^.05677 
of  the  quotient. 


DECIMAL  FEACTIONS  89 

Buying  and  Selling  by  the  Hundred 
oral  exercise 

1.  Compare  460  ^  100  x  $2  with  4.60  x  f  2. 

2.  Find  the  cost  of  450  lb.  of  guano  at  $4  per  cwt. 

3.  Find  the  cost  of  600  lb.  of  wire  nails  at  34^  per  cwt. 

4.  Find  the  cost  of  4950  paving  stones  at  18  per  C. 

Solution.     C  stands  for  100.    4950  paving  stones  are  49.5  times  4y.O 

100  paving  stones.     Since  1  hundred  paving  stones  cost  $8,  49.5  8 

hundred  paving  stones  will  cost  49.5  times  ^8,  or  $396.  396^ 

WRITTEN    EXERCISE 


Find  the  cost  : 

Quantity 

Price  per 
Hundredweight 

Quantity 

Price  per 
Hundredweight 

1.    450  1b. 

55^ 

5. 

1600  lb. 

71^ 

2.    510  1b. 

77^ 

6. 

2600  lb. 

15>> 

3.    640  1b. 

60^ 

7. 

4900  lb. 

"JOp 

4.    330  1b. 

5Q^ 

8. 

3100  lb. 

88j* 

Buying  and  Selling  by  the  Thousand 

ORAL  exercise 


1.  Compare  3500  -v- 1000  x  19  with  3.500  x  $9. 

2.  Compare  12200  --  1000  x  $5  with  12.2  x  15. 

3.  Find  the  cost  of  7150  feet  of  lumber  at  $11  per  M. 

Solution.     M  stands  for  thousand.     7150  feet  are  7.15  times  7.15 

1000  feet.    Since  1  thousand  feet  of  lumber  cost  $11,  7.15  thousand  11 

feet  will  cost  7.15  times  $11,  or  $78.65.  78^65 

Mnd  the  cost  of: 

4.  8500  tiles  at  $8  per  M ;  at  8  9  per  M. 

5.  4500  bricks  at  $6  per  M  ;  at  17  per  M, 

6.  7500  shingles  at  812  per  M  ;  at  814  per  M. 

7.  3200  ft.  lumber  at  814  per  M ;  at  812  per  M. 

8.  15,000  ft.  lumber  at  811  per  M  ;  at  812  per  M. 

9.  12,000  ft.  lumber  at  816  per  M  ;  at  815  per  M. 


90  CONCISE   BUSINESS   ARITHMETIC 

Buying  and  Selling  by  the  Ton  of  2000  Pounds 
oral  exercise 


1.  Compare  8000  -f-  2000  x  8  with  8000^1000  x  4. 

2.  Compare  7000  -v-  2000  x  18  with  7x9. 

3.  Find  the  cost  of  4250  lb.  coal  at  S8  per  ton. 

Solution.     4250  lb.  is  4.25  times  1000  lb.     If  the  cost  of  2  thou-         4.25 
sand  pounds  is  |8,  the  cost  of  1  thousand  pounds  is  $4.     Since  A 


17.00 


1  thousand  pounds  of  coal  cost  $4,  4.25  thousand  pounds  will  cost 
4.25  times  |4,  or  $17. 

WRITTEN   EXERCISE 

1.  At  S9  per  ton,  find  the  cost  of  the  hay  in  the  following 
weigh  ticket.     Also  find  the  cost  at  S8.75  per  ton. 


SCALES  OF  E.  H.  ROBINSON  &  CO. 

^    y/OO    ^°^^  of  xyr^^y r>. 

From  ^,,C^A/^^i^^/^^  To   ^/jJ. .TJtT^^ ST^^ 

Gross  weight     ^^//^      lb. 
Tare     /  <r  ^  ^      Ih. 


Net  weight     Z-f^jTO^  lb.       .    .     ^^ 


Weigher 


2.  At  S  7.50  per  ton  find  the  cost  of  the  coal  in  the  following 
weigh  ticket.     Also  find  the  cost  at  S6.95  per  ton. 


WELLINGTON -WILD  COAL  CO, 

126  Main  Street.  Rochester,  N.  Y. 


3^ ^  //^^r^-y;^..i^-^  t^yf^A-iT^.^  ^~Y?^^y 
Teamster  y/7.^^r7,y?^.^7^^,  Receioed  by   C.lYl..  \\.yCnH/r\.  h<m^ 


DECIMAL   FRACTIONS  91 

3.  What  will  8650  lb.  of  hay  cost  at  $12  per  ton? 

4.  Find  the  cost  of  2150  lb.  of  coal  at    $6    per    ton. 

5.  At  132  per  ton,  what  is  the  cost  of  26,480  lb.  of 
phosphate  ? 

6.  Find  the  cost  of  54,260  pounds  of  coal  at  $5.80  per  ton. 

7.  Find  the  cost  of  12  loads  of  coal  weighing  4100,  3900, 
4306,  4100,  4060,  4300,  3286,  3980,  3850,  4130,  3700,  3950  lb. 
net,  at  $5.20  per  ton. 

8.  Find  the  total  cost  of  :  5265  lb.  hard  coal  at  $8.40  per  ton ; 
12,200  lb.  soft  coal  at  $3  per  ton;  8275  lb.  cannel  coal  at  $11.75 
per  ton;  34,160  lb.  egg  coal  at  $6.20  per  ton;  12,275  lb.  nut 
coal  at  $5.75  per  ton;  8753  lb.  grate  coal  at  $5.80  per  ton; 
24,160  lb.  stove  coal  at  $6.50  per  ton. 

9.  During  the  month  of  January,  in  a  recent  year,  there  were 
consumed  in  a  manufacturing  plant  72  loads  of  coal  weighing  as 
follows:  6100,  6500,  6700,  6840,  7210,  6680,  7250,  8400, 
6100,  6100,  6250,  6380,  6480,  6300,  6500,  6160,  6410,  6370, 
6410,  6570,  .6480,  6240,  6370,  6430,  6480,  6300,  7400,  7580, 
7620,  7240,  7110,  7220,  7420,  7480,  6390,  6100,  6250,  6250, 
6900,  6270,  6280,  6290,  6270,  6390,  6420,  6120,  6120,  6200, 
6300,  6120,  6430,  6430,  8100,  6100,  6200,  6310,  6204,  6160, 
6170,  6240,  6390,  6140,  6240,  7190,  7240,  7140,  7200,  6340, 
8420,  6310,  7420,  6120  lb.  net.  Find  the  cost  at  $5.87J 
per  ton. 

WRITTEN  REVIEW  EXERCISE 

1.  Of  what  number  is  25.56  both  the  divisor  and  quotient? 

2.  The  sum  of  the  divisor  and  quotient  is  414.06.  If  the 
divisor  is  .6,  what  is  the  dividend? 

3.  In  what  time  will  3  boys  at  $  .75  per  day  earn  as  much 
as  2  men  earn  in  75  da.  at  $2.25  per  day? 

4.  A  merchant  sold  a  quantity  of  flour  for  $370  and  realized 
a  gain  of  $34.  If  the  selling  price  was  $7.40  per  barrel,  what 
was  the  cost  per  barrel  ? 

CB 


92  CONCISE   BUSINESS   ARITHMETIC 

5.  What  number  is  that  which  is  165  times  as  great  as 
82.5? 

6.  If  450  bbl.   of  beef  sold  for  $5872.50,  what  was   the 
selHng  price  per  hundred  barrels  ? 

7.  What  will  be  the  cost,  at  15/  per  yard,  of  a  paper  border 
for  a  room  8  yd.  wide  and  12  yd.  long? 

8.  An  article  was  sold  for  $22.50 ;  if  i  of  the  cost  was  lost, 
what  was  the  loss  ? 

9.  Wood  costing  $3.50  per  cord  is  sold  for  $4.10  per  cord. 
How  many  cords  must  be  handled  to  gain  $240  ? 

10.  Fmd  the  cost  of  8  bbl.  of  pork  weighing  280,  281,  286, 
290,  285,  277,  285,  and  290  lb.  net,  at  $8.50  per  hundred 
pounds. 

11.  A  flock  of  200  sheep  was  bought  for  $700.  Ten  of  the 
sheep  died,  and  the  remainder  of  the  flock  was  sold  at  $3.95  per 
head.     What  was  the  gain  or  loss  ? 

12.  If  the  actual  cost  of  the  necessities  of  life  for  one  person, 
in  a  given  year,  amounted  to  $81.45,  and  10  yr.  later,  owing  to 
the  advance  in  prices,  the  same  necessities  cost  $108.60,  what 
was  the  fractional  increase  in  the  cost  of  living  ? 

13.  A,  B,  and  C  bought  a  stock  of  goods  for  $  7500,  A  con- 
tributing $2500,  B  $3000,  and  C  the  remainder.  They  sold  the 
goods  for  $8400  and  divided  the  profits  equally.  How  much 
of  the  $8400  should  A,  B,  and  C,  respectively,  receive  ? 

14.  The  following  were  the  transactions  of  a  merchant  for 
1  mo.:  merchandise  on  hand  July  1,  $3378.50,  sold  for  cash, 
$2374.20;  bought  for  cash,  $1945. 35;  sold  on  account,  $2276.30; 
bought  on  account,  $876.40 ;  on  hand  July  31,  $2056.35.  Ex- 
penses for  the  month,  $284.25.  What  was  the  net  gain  for 
the  month? 

15.  The  following  were  the  transactions  of  a  merchant  for 
1  mo.:  merchandise  on  hand  January  1,  $8120.90;  bought  for 
cash,  $3265.90;  bought  on  account,  $2845.10;  sold  for  cash, 
$5157.65;  sold  on  account,  $4218.25;  on  hand  January  31, 
$7253.25.  The  sale  to  Jas.  S.  Greet,  on  account,  cannot  be 
collected,  $51.20.     What  was  the  net  gain  for  the  month? 


DECIMAL  FRACTIONS  93 

16.  What  is  the  total  freight  on  12,250  lb.  of  hardware  at 
$.65  per  hundredweight  and  15,670  lb.  of  hardware  at  1.60 
per  hundredweight? 

17.  A  merchant  bought  250  yd.  of  cloth  at  $3.50  per  yard, 

and  150  yd.  at  $4.25.     At  what  average  price  per  yard  should 
the  whole  be  sold  to  realize  an  average  profit  of  f  1  per  yard  ? 

18.  What  is  the  cost  of  25  bbl.  of  sugar  containing  312,  304, 
309,  317,  330,  325,  315,  318,  317,  305,  319,  320,  325,  330,  335, 
330,  325,  315,  315,  320,  320,  330,  330,  315,  315  lb.  net,  at  5|^ 
per  pound  ? 

19.  A  received  11088  from  the  sale  of  his  barley  crop.  If  he 
received  10.85  per  bushel  for  the  barley  and  his  farm  produced 
an  average  of  32  bu.  to  the  acre,  how  many  acres  did  it  take 
to  produce  the  barley? 

20.  A  manufacturing  pay  roll  shows  that  40  hands  are  em- 
ployed at  S1.45  per  day,  50  hands  at  $1.40  per  day,  10  hands 
at  ^3  per  day,  40  hands  at  $2.50  per  day,  and  5  hands  at  |8 
per  day.     Find  the  average  daily  wages. 

21.  A  hardware  merchant  found  that  his  stock  of  goods, 
Jan.  1,  amounted  to  134,350.65.  During  the  year  he  bought 
goods  amounting  to  $211,165.45,  and  sold  goods  amounting  to 
$220,540.45.  Dec.  31,  he  took  an  account  of  stock  and  found 
that  the  goods  on  hand  at  cost  prices  were  worth  $81,275.64. 
What  was  his  gain  or  loss  for  the  year? 

22.  Without  copying  the  following  figures,  find  (a)  the  sum 
of  each  line,  and  (6)  the  sum  of  each  column.  Prove  the  work 
by  adding  the  line  totals  and  comparing  the  sum  with  the  sum 
of  the  column  totals. 


17.035 

18.0135 

186.02 

126.42 

.      6.009 

8.005 

5.07 

142.004 

.0634 

3.14 

32.972 

18.0981 

165.42 

1.7538 

9.314 

126.83 

4.931 

.628 

6.75 

.048 

95.16 

6.815 

.8467 

8.41 

.062 

101.215 

21.214 

21.221 

2.61 

18.641 

94 


CONCISE   BUSINESS   ARITHMETIC 


A   REVIEW   TEST 


Without  copying,  find  the  quotients  and  the  sum  of  the  quotients, 
in  each  problem.      Time,  approximately,  forty  minutes. 

In  these  problems  the  quotient  in  each  division  is  apparent  at  a  glance, 
hence  the  attention  is  fixed  on  placing  the  decimal  point. 


1. 

2. 

3. 

12.5^5 

96 -f- .4 

3.9 -5- .3 

1.25  -^  .5 

.96- 

-.004 

39-f-.03 

.125-^.5 

9.6- 

-4 

3.9  -4-  .003 

.125-^.05 

.96- 

-.04 

.0039-^.003 

.0125-^5 

9.6- 

-.04 

.039 -4- .0003 

125 -f- .5 

960 -5- .4 

390^.3 

12.5-^.05 

.096  ^  .04 

3.9-4-3 

.0125-^.005 

960  -^  .004 

390 -i- .03 

12.5-^.005 

9.6  -5-  .04 

39 -5- .003 

4. 

5. 

6. 

.0065-^1.3 

.69  H-  23 

.085-5- .17 

6.5  -^  1.3 

690  -^  2.3 

.85 -5- .017 

.65-^.13 

6.9  -i-  23 

8.5 -4- .017 

65  H- .013 

6.9  -^  2.3 

.85-^.0017 

6.5-^130 

.69  -H  230 

85^.17 

65-1-130 

.0069  -^  .23 

.085-1- .0017 

6.5-^1300 

6.9  -f-  230 

8.5^1.7 

.65-5-13 

.069-^.0023 

85-5-1700 

6500^130 

690-5-2300 

8.5-5-170 

7. 

8. 

9. 

5.7 -f- .19 

75-^.25 

55 -f.  1.1 

57^.019 

75 -f- 2.5 

550-5-1.1 

570-^1.9 

.75-^2.5 

.055-5-110 

57^190 

7.5-4-250 

5.5 -f- 110 

.0057-1-1.9 

.75 -5- .25 

55^110 

5.7-^190 

75^.025 

.055^.011 

57^.19 

.75  ^  250 

550  -5-  .11 

.57  -f- 190 

7.5 -4- .025 

550  -5- 1100 

CHAPTER  VIII 

FACTORS,    DIVISORS,   AND   MULTIPLES 

FACTOES 
ORAL  EXERCISE 

1.  Name  two  factors  of  63  ;  of  88  ;  of  144  ;  of  128. 

2.  What  are  the  factors  of  49?  of  77?  of  35?  of  21? 

3.  Name  three  factors  of  45;  of  66;  of  24;  of  60;  of  80. 

4.  Name  a  factor  that  is  common  to  35  and  77;  36,  63,  and  81. 

5.  Name  three  factors  that  are  common  to  30,  60,  and  210. 

6.  Which  of  the  following  numbers  have  no  factors  except 
itself  and  one  ?     11,  27,  15,  37,  49,  62,  73,  81,  23. 

110.  An  even  number  is  an  integer  of  which  two  is  a  factor. 
An  odd  number  is  an  integer  of  which  two  is  not  a  factor. 
A  prime  number  is  a  number  that  has  no  integral  factor  except 
itself  and  one.  A  composite  number  is  a  number  that  has  one 
or  more  integral  factors  besides  itself  and  one. 

Numbers  are  mutually  prime  when  they  have  no  common  factor  greater 
than  one. 

WRITTEN  EXERCISE 

1.  Make  a  list  of  all  the  odd  numbers  from  1  to  100  in- 
clusive;  of  all  the  prime  numbers;  of  all  the  even  numbers; 
of  all  the  composite  numbers. 

ORAL  EXERCISE 

1.  Is  2  a  factor  of  28?  of  125?  of  42?  of  49?  By  what 
means  do  you  readily  determine  this  ? 

2.  Is  5  a  factor  of  125  ?  of  170  ?  of  224  ?  of  1255  ?  of  1056  ? 
By  what  means  do  you  readily  determine  this  ? 

3.  When  is  a  number  divisible  by  10?  by  3  ?  by  9  ? 

96 


96  COKCISE  BUSIKESS   ARITHMETIC 


Tests  of  Divisibility  of  Numbers 

111.  A  number  is  divisible  by: 

1.  Two,  when  it  is  even,  that  is,  when  it  ends  with  0,  2,  4,  6,  or  8. 

2.  Three,  when  the  sum  of  its  digits  is  divisible  by  3. 

3.  Four,  when  the  number  expressed  by  its  two  right-hand  figures  is 
divisible  by  4. 

4.  Fioe,  when  it  ends  with  0  or  5. 

5.  Six,  when  it  is  even  and  the  sum  of  its  digits  is  divisible  by  3. 

6.  Eight,  when  the    number  expressed  by  the  last  three   right-hand 
figures  is  divisible  by  8. 

7.  Nine,  when  the  sum  of  its  digits  is  divisible  by  9. 

8.  Ten,  when  its  right-hand  figure  is  a  cipher. 

ORAL  EXERCISE 

Name  one  or  more  factors  of  each  of  the  following  numbers: 

1.  184.       5.  6984.       9.  51625.     13.  14128. 

2.  2781.       6.  2750.      10.  83870.     14.  66438. 

3.  1449.       7.  8975.      ii.  13599.      15.  31284. 

4.  638172.     8.  71168.     12.  123125.     16.  17375. 

Factoring 

112.  Factoring  is  the  process  of  separating  a  number  into  its 
factors. 

113.  Example.    Find  the  prime  factors  of  780. 

Solution.    Since  the  number  ends  in  a  cipher,  divide  it  by  the  prime 

factor  6 ;  since  the  resulting  quotient  is  an  even  number,  divide  it  by  2. 

Since  78  is  an  even  number,  divide  it  by  2  ;  since  the  sum  of  the  digits 

in  the  resulting  quotient  is  divisible  by  3,  divide  by  3.    The  prime 

factors  are  then  found  to  be  5,  2,  2,  3,  and  13. 

.lo 

WRITTEN  EXERCISE 

Find  the  prime  factors  of: 

1.  112.  4.  786.  7.  968.  10.  408.  13.  2718.  16.  6900. 

2.  126.   5.  392.  8.  689.  11.  650.  14.  3240.  17.  2064. 

3.  288.  6.  315.  9.  1098.  12.  762.  15.  3205.  18.  7400. 


5 

2 
2 
3 

780 

156 

78 

39 

FACTORS,  DIVISORS,   AND  MULTIPLES  97 

Cancellation 
oral  exercise 
1.    (4xl5)-f-(4x3)  =  15-f-3.     Why? 


2.    Divide  2x5x7  by  5x2;  8x7x5  by  5x2x7. 
3    3x7x8^  ^      5x2x8x3^  ^        2x9x7x5^.> 
7x3  '  2x8x3         '        5x7x2x3' 

4.  What  effect  on  the  quotient  has  rejecting  equal  factors 
in  both  dividend  and  divisor  ? 

114.  Cancellation  is  the  process  of  shortening  computations 
by  rejecting  or  canceling  equal  factors  from  both  dividend  and 
divisor. 

115.  Example.  Divide  the  product  of  6,  8, 12,  32,  and  84  by 
the  product  of  3,  4,  6,  and  24. 

2     2      2       4      28 

6xgx;2x32x?4 

^^^^^^^  =  2x2x2x4x28=896. 

Solution.  Do  not  form  the  products,  but  indicate  the  multiplication  by 
the  proper  signs  and  write  the  divisor  below  the  dividend  as  shown  above.  3,  4, 
and  6  in  the  divisor  are  factors  of  6,  8,  and  12,  respectively,  in  the  dividend ; 
hence,  reject  3,  4,  and  6  in  the  divisor  and  write  2,  2,  and  2,  respectively,  in  the 
dividend ;  then  cancel  the  common  factor  8  from  24  in  the  divisor  and  32  in  the 
dividend,  retaining  the  factors  3  and  4,  respectively  ;  next  cancel  the  common 
factor  3  in  the  divisor  from  84  in  the  dividend  and  there  remains  the  uncanceled 
factors  2,  2,  2,  4,  and  28  in  the  dividend.  Hence,  the  quotient  is2x2x2x4 
X  28,  or  896. 

WRITTEN  EXERCISE 


1.   14x21x48^7x21x6  =  ? 


2.  128  X  48  X  88  -V-  64  X  24  X  4  =  ? 

3.  Divide  128  x  18  x  36  by  64  x  18  x  12. 
^    12  X  16x24  X  8x92x28^  y 

6  X  8  X  23  X  7 


98  CONCISE   BUSINESS   ARITHMETIC 

5.  If  18  T.  of  hay  cost  $270,  what  will  25  T.  cost  at  the 
same  rate  ? 

6.  How  many  days'  work  at  $2.75  will  pay  for  2  A.  of 
land  at  $110  per  acre? 

7.  If  75  bbl.  of  flour  may  be  made  from  375  bu.  of  wheat, 
how  many  bushels  will  be  required  to  make  120  bbl.  of  flour  ? 

8.  If  45  men  can  complete  a  certain  piece  of  work  in  120 
da.,  how  many  men  can  complete  the  same  piece  of  work  in 
30  da.? 

9.  The  freight  on  350  lb.  of  evaporated  apricots  is  $1.47. 
At  that  rate  how  much  freight  should  be  paid  on  7350  lb.  of 
evaporated  apricots? 

10.  If  15  rm.  of  paper  are  required  to  print  400  copies  of 
a  book  of  300  pp.,  how  many  reams  will  be  required  to  print 
32,000  copies  of  a  book  of  300  pp.  ? 


DIVISORS   AND  MULTIPLES 
Common  Divisors 

oral  exercise 

1.  Name  a  factor  that  is  common  to  35  and  49. 

2.  Name  two  factors  that  are  common  to  both  48  and  64. 

3.  Name  the  greatest  factor  that  is  common  to  75  and  100. 

116.  A  common  divisor  is  a  factor  that  is  common  to  two  or 
more  given  numbers.  The  greatest  common  divisor  (g.  c.  d.)  is 
the  greatest  factor  that  is  common  to  two  or  more  given  numbers. 

117.  Example.     Find  the  g.  c.  d.  of  24,  84,  and  252. 

Solutions,     (a)  Separate  each  of  the  num- 
bers into  its  prime  factors.    The  factor  2  occurs  (j*) 
twice  in  all  the  numbers  and  the  factor  3  once  24=  2x2x2x3 
in  all  the  numbers.    None  of  the  other  factors  84  =2x^x3x7 
occur  in  all  the  numbers;  hence,  2  x  2  x  3,  or  ^_^  __  ^       ^       „       ^       „ 
12,  is  the  greatest  common  divisor  of  24,  84,  ^"^^  =  lX^Xoy.6X  i 
and  252, 


FACTORS,  DIVISORS,  AND  MULTIPLES  99 

(b)  The  common  prime  factors  of  two  or  more  given  ('5\ 

numbers  may  be  found  by  dividing  the  numbers  by  their  9^24  —  84—2^2 

prime  factors  successively  until  the  quotients  contain  no  ^rr^^ ~r: 

common  factor,  as  shown  in  the  margin.  Z^IZ  —  41  —  Izb 

Ever  since  decimal  fractions  came  into  quite  gen-  -^ — 

eral  use  the  subject  of  greatest  common  divisor  has  "^  *  •^-*- 

been  stripped  of  most  of  its  practical  value.  When  fractions  like  i||^  were 
quite  generally  used,  it  was  necessary  to  reduce  them  to  their  lowest  terms 
before  they  could  be  conveniently  handled  in  an  operation.  For  this  pur- 
pose, the  greatest  common  divisor  (here  97)  was  found  and  canceled  from 
each  term,  thus  greatly  simplifying  the  fraction  (here  if).  Now,  however, 
the  greatest  common  divisor  of  the  terms  of  the  fractions  used  in  business 
is  easily  found  by  inspection,  and  the  need  for  finding  the  greatest  common 
divisor  is  slight. 

ORAL  EXERCISE 

1.  What  is  the  greatest  common  divisor  of  65  and  75?  of  12 
and  32?  of  75  and  125? 

2.  What  is  the  greatest  common  divisor  of  12,  30,  and  96? 
of  8,  24,  and  42?  of  36,  90,  and  96? 

3.  What  divisor  should  be  used  in  reducing  -ff^  to  its 
lowest  terms?   iff?   ^%\?   ^\%?    ^^V?    2%? 

WRITTEN    EXERCISE 

Find  the  greatest  common  divisor  of: 

1.    48,  240.  2.   42,  28,  144.  3.   88,  144,  220. 

4.  A  real  estate  dealer  has  four  plots  of  land  which  he  wishes 
to  divide  into  the  largest  number  of  building  lots  of  the  same 
size.  If  the  plots  contain  168,  280,  182,  and  252  square  rods, 
respectively,  how  many  square  rods  will  there  be  in  each  build- 
ing lot? 

Common  Multiples 

oral  exercise 

1.  Name  a  multiple  of  7  ;  of  9;   of  16 ;  of  64. 

2.  Name  two  other  multiples  of  each  of  the  above  numbers. 

3.  Name  two  multiples  that  are  common  to  3  and  4 ;  to  5 
and  9 ;  to  8  and  12.  Which  of  the  multiples  just  named  is  the 
least  common  multiple? 


5)14 

21 

42 

3)7 

21 

21 

7)7 

7 

7 

100  CONCISE   BUSINESS   ARITHMETIC 

118,  A  common  multiple  is  any  integral  number  of  times  two 
or  more  given  numbers.  The  least  common  multiple  (1.  c.  m.) 
of  two  or  more  numbers  is  the  least  number  which  is  an  integral 
number  of  times  each  of  the  given  numbers. 

119.  Example.     Find  the  1.  c.  m.  of  28,  42,  and  84. 

Solutions,    (a)  Resolve  each  of  the  numbers  into  (^) 

its  prime  factors.     The  factor  2  occurs  twice  in  28  and      98  =  2x2x7 

in  84,  the  factor  3  occurs  once  in  42  and  84,  the  factor  7       .^       ^       ^       - 

A*}  —  ^  y  o  y  7 
occurs  once  in  each  of  the  numbers.     Therefore,  the 

least  common  multiple  is  2  x  2  x  3  x  7,  or  84  ;  or  84  =  2  X  2  X  3  X  7 

(6)   Arrange  the  numbers  in  a  horizontal  line  and  divide 
by  any  prime  factor  that   will   exactly  divide  any  two  of  \^) 

them.  Divide  the  numbers  in  the  resulting  quotient  by  any  2)  28  42  84 
prime  factor  that  will  divide  any  two  of  them,  and  so  con- 
tinue the  operation  until  quotients  are  found  that  are  prime 
to  each  other.  Find  the  product  of  the  several  divisors  and 
the  last  quotients  and  the  result  is  the  l.c.m.  2x2x3x7 
=  84,  the  L  c.  m.  Ill 

All  numbers  that  are  factors  of  other  given  numbers  may 
be  disregarded  in  finding  the  1.  c.  m.       Thus  the  common  multiples  of  4,  8, 
16,  32,  64,  and  80  are  the  same  as  the  multiples  of  04  and  80. 


ORAL  EXERCISE 

State  the  least  common  multiple  of: 

1.  6,  5,  and  3.  4.  2,  4,  7,  8,  48,  24. 

2.  6,  8,  12,  and  24.  5.  6,  42,  84,  168,  336. 

3.  4,  5,  15,  and  30.  6.  5,  15,  75,  150,  300. 

WRITTEN  EXERCISE 

Find  the  least  common  multiple  of: 

1.  6,  7,  8,  and  5.  5.    4,  20,  12,  and  48. 

2.  6,  18,  24,  and  84.  6.    62,  78,  30,  and  142. 

3.  12,  24,  36,  and  96.  7.    35,  105,  125,  and  225. 

4.  32,  46,  92,  and  128.  8.    114,  240,  72,  and  320. 
9.    What  number  is  that  of  which  2,  3,  5,  and  11  are  the 

only  prime  factors? 


CHAPTER  IX 

COMMON  FRACTIONS 
ORAL  EXERCISE 

1.  When  a  quantity  is  divided  into  3  equal  parts,  what  is 
each  part   called?  into  8  equal  parts?  into  12  equal  parts? 

2.  The  shaded  part  of  A  is  what  part  of  the  whole  hexagon  ? 
the  shaded  part  of  B  ?  the  shaded  part 
of  C? 

3.  In  the   shaded   part  of   A  how 
many  sixths  ?  in  the  shaded  part  of  B  ? 

4.  One  half  of  the  hexagon  is  how  many  sixths  of  it? 
How  many  sixths  in  the  whole  hexagon? 

5.  In  the  unshaded  part  of  B  how  many  thirds?  Two  thirds 
are  how  many  sixths? 

6.  In  the  unshaded  part  of  C  how  many  sixths? 

7.  Read  the  following  fractions  in  the  order  of  their  size, 
the  largest  first :  ^,  f ,  |,  |,  1,  ^,  1 

8.  Complete  the  following  statement :  Such  parts  of  a  unit 
as  .5,  .25,  J,  |,  etc.,  are  called  . 

120.  Common  fractions  are  expressed  by  two  numbers,  one 
written  above  and  one  below  a  short  horizontal  line. 

121.  The  number  written  above  the  line  is  called  the 
numerator  of  the  fraction,  and  the  number  written  below, 
the  denominator  of  the  fraction. 

122.  The  numerator  tells  the  number  of  parts  expressed  by 
the  fraction ;  the  denominator  names  the  parts  expressed  by 
the  fraction. 

Thus,  in  the  fraction  f,  4  tells  that  a  number  has  been  divided  into 
four  equal  parts  and  3  shows  that  three  of  these  parts  have  been  taken. 

101 


":I02  ^  dONCISE   BUSINESS   ARITHMETIC 

'  ''  1^3.'  'It  1^  td'^ar  that  the  greater  the  number  of  equal  parts  into 
which  a  unit  is  divided,  the  smaller  is  each  part ;  and  the  fewer 
equal  parts  into  which  a  unit  is  divided,  the  greater  the  size  of 
each  part.    Hence, 

Cf  two  fractions  having  the  same  denominator^  the  one  having 
the  greater  numerator  expresses  the  greater  value;  and 

Of  two  fractions  having  the  same  numerator^  the  one  having  the 
smaller  denominator  expresses  the  greater  value, 

124.  The  terms  of  a  fraction  are  the  numerator  and  denomi- 
nator. 

125.  A  unit  fraction  is  a  fraction  whose  numerator  is  one. 

Thus  \,  \,  \,  and  J^  are  unit  fractions.     \  in.  is  read  one  third  of  an  inch. 

126.  An  improper  fraction  is  a  fraction  whose  numerator 
is  equal  to  or  greater  than  its  denominator. 

Thus,  I,  f,  and  ^/.  are  improper  fractions.  The  value  of  an  improper 
fraction  is  always  equal  to  or  greater  than  one. 

127.  A  mixed  number  is  the  sum  of  a  whole  number  and 
a  fraction. 

Thus,  2\  and  4|,  read  two  and  one  seventh  and  four  and  two  ffths,  are 
mixed  numbers. 

ORAL  EXERCISE 

1.  What  takes  the  place  of  the  denominator  in  .5?  in  .25? 

2.  Read  aloud  the  following  fractions  in  the  order  of  their 
size,  the  largest  first :  |,  -jL  h  h  h  i6'  6'  h  2V'  2V'  ih' 

3.  Read  aloud  the  following  fractions  in  the  order  of  their 
size,  the  smallest  first :  |,  |,  J,  f ,  1  |,  -j^,  A,  f,  1  Jg ,  f . 

4.  Read  aloud  the  following:  J  mi.;  |T.;  21^  yd.;  ij^'S 
cu.  ft.;  275f  A.;  250^5^  lb.;  X  IS^^^  ;  <£  2711 ;   ^^^  sq.  ft. 

5.  Of  all  the  cotton  produced  in  the  United  States  in  a  recent 
year  the  principal  cotton-growing  states  contributed  approxi- 
mately as  follows :  North  Carolina,  ^^^ ;  South  Carolina,  ^ ; 
Georgia,  I ;  Oklahoma  and  Indian  Territory,  Jg^ ;  Alabama,  I ; 
Mississippi,  -Jg  ;  Louisiana,  -^^ ;  Texas,  ^ ;  Arkansas,  Jy ;  Ten- 
nessee, ^^g.  Name  the  principal  cotton-growing  states,  in  the 
order  of  production,  for  that  year. 


u 

^ 

'^A 

^1 

yA 

yA 

^ 

W\ 

^^ 

'm^ 

m$ 

^ 

'Mmm. 

w/Mim 

1 

yMW/Mmmm. 

1 

COMMON   FRACTIONS  103 

REDUCTION 
To  Higher  Terms 

ORAL  EXERCISE 

1.  How  many  halves  in  1  ?  how  many  fourths  ?  how  many 
eighths  ?  how  many  sixteenths? 

2.  How  many  fourths  in  J? 
how  many  eighths?  how  many 
sixteenths  ? 

3.  How  many  eighths  in  \  ?  how  many  sixteenths  ? 

4.  How  many  fourths  in  ^|  ?  how  many  eighths  in  i|  ?  how 
many  halves  in  ^^g  ? 

5.  What  effect  is  produced  upon  the  value  of  a  fraction  by 
multiplying  or  dividing  both  terms  of  a  fraction  by  the  same 
number  ? 

6.  Change  14  gal.  to  quarts.  Compare  the  size  of  the  units 
in  14  gal.  with  the  size  of  the  units  in  56  qt.  ;  the  number  of 
units  ;  the  value  of  the  two  numbers. 

7.  Change' 1  to  twelfths;  J;  i;  J;  §;  f;  f- 

8.  Name  three  fractions  equal  in  value  to  |^ ;  to  | ;  to  |. 

128.  It  has  been  seen  that  multiplying  or  dividing  both  terms 
of  a  fraction  hy  the  same  number  does  not  change  the  value  of  the 
fraction. 

129.  A  fraction  is  reduced  to  higher  terms  when  the  given 
numerator  and  denominator  are  expressed  in  larger  numbers. 

ORAL  EXERCISE 

1.  Reduce  to  twelfths :  ^,  |,  |. 

2.  Reduce  to  sixteenths :  |,  \,  J,  f . 

3.  Reduce  to  twentieths :  |,  -|,  -f^,  |,  f . 

4.  Reduce  to  twenty-fourths :  |,  |,  |,  -^,  f ,  f . 

5.  Reduce  to  thirty-seconds :  J,  f ,  f ,  |,  yV^  yV^  -^6'  tV* 

6.  Reduce  to  one-hundredths  :  |,  J,  f ,  -j^,  2V  ^'  \'  A* 

7.  Reduce  |  and  f  to  fractions  having  the  denominator  24. 


104  CONCISE  BUSINESS  ARITHMETIC 


To  Lowest  Terms 

ORAL  EXERCISE 

1.  ^  equals  how  many  thirds?  1|  equals  how  many  halves? 

2.  Name  the  largest  possible  unit  frac- 
tion. Why  is  this  the  largest  possible 
unit  fraction? 

3.  Change  -^^  *^  *^^  largest  possible 


unit  fraction;  y8_;  _2^_.;  _5_o_.  J^2^.    Express  -l|  in  its  simplest 
form.     Reduce  ^^q  to  its  lowest  terms. 

130.  A  fraction  is  reduced  to  its  lowest  terms  when  the 
numerator  and  denominator  are  changed  to  numbers  that  are 
mutually  prime. 

131.  Example.    Reduce  -^^^  to  its  lowest  terms. 

Solution.  6  is  a  common  factor  of  96  and  108  ;  dividing 
both  terms  by  6,  the  result  is  |f.  2  is  a  common  factor  of 
16  and  18 ;  dividing  both  terms  by  2,  the  result  is  |. 


1%  —  11 


ORAL  EXERCISE 

1.  Reduce  to  fifteenths :  ^,  -|,  |,  |. 

2.  Reduce  to  eighths :  ^\,  -|-,  |,  if,  1|,  |. 

3.  Reduce  to  fiftieths :  |-,  |,  j%%,  -^,  -/g,  J^. 

4.  Change  to  twentieths :  ^  -^^  |,  |,  l  -^%,  f . 

5.  Reduce  to  lowest  terms :  ^g,  y^^,  ^^^  ||,  -^^,  f . 

WRITTEN  EXERCISE 

1.  Reduce  to  sixteenths  :  IJ^,  ^|^,  |,  f|,  f ,  J|§. 

2.  Reduce  to  lowest  terms:  -^^^^  cu.  ft.,  -^^-^  A.,   ^^^^-^  T. 

3.  Reduce  to  lowest  terms:  J|§  mi.,  £l|f,  fff^  lb.,  |f  mi. 

4.  Reduce  to  three-hundred-twentieths :  |  mi.,  ^  mi.,  Jg   mi. 

5.  Reduce  to  their  simplest  common  fractional  form  :  |^f|^  T., 
hin  T.,  ^  A.,  l|^  A.,  IIJ  sq.  mi.,  f  |f  sq.  mi.,  §|^  mi. 


COMMON  FRACTIONS  105 


Integers  and  Mixed  Numbers  to  Improper  Fractions 

oral  exercise 

1.  How  many  quarts  in  1  gal.?     in  3  gal.? 

2.  How  many  sixths  in  1?     in  3?     in  5?     in  7? 

3.  How  many  fifths  in  1?     in  1|?     in  If?     in  3J? 

4.  Express  as  fourths :  6J,  12|,  13,  87,  61^,  281 

5.  Express  as  eighths :  15,  12,  lOJ,  1^,   2|,  If,  9J. 

6.  Express  as  halves :  27,  14,  301    1711    1821,  249. 

WRITTEN  EXERCISE 

Reduce  to  improper  fractions : 

1. 
2. 


83J. 

4.    666|. 

7.    266jV. 

10. 

3150f. 

166|. 

5.    180^. 

8.    319^5. 

11. 

16251. 

333J. 

6.    212Jj. 

9.   146ii. 

12. 

2150,^ 

Improper  Fractions  to  Integers  or  Mixed  Numbers 
oral  exercise 

1.  How  many  pecks  in  240  qt.  ?    ^|^  =  ?     ^^  =  ? 

2.  Change  to  integers :  1|^,  1|^,  ^^-,   2_8_8.,  A|5JI,  l||iL. 

3.  Express  28 J  as  fourths ;  express  ^\^  as  a  mixed  number. 

4.  Change   to   mixed   numbers:      ^{^,   ij^,   1|^,   -Ifl,   ^. 

5.  What  is  the  value  of:  ^-^  lb.?  ^^-^-  lb.?  1|^  bu.?  ^fk  p^.? 
^^  ft.?  ^-if  A.?  11^  mi.?  ^5_(i  lb.?  1||  sq,  ft.? 

written  exercise 
Reduce  to  integers  or  mixed  numbers: 
1.    fit  mi.  4. 

3      95.55.  T  6 

132.  When  expressing  final  results  reduce  all  proper  frac- 
tions to  their  lowest  terms  and  all  improper  fractions  to 
integers  or  mixed  numbers. 


^¥A. 

7.   241  a  lb. 

im  T. 

8.     -1111  CU.  ft. 

ffl*T. 

9.    ^V^sq.  mi 

106  CONCISE   BUSINESS   AKITHMETIG 

To  Least  Common  Denominator 

ORAL  EXERCISE 

1.  How  many  pounds  in  1  T.  500  lb.  ?  5  T.  +  1000  lb.  =  ?  lb. 
6  T.  1000  lb.  =  ?  T. 

2.  How  must  numbers  be  expressed  before  they  can  be 
added  or  subtracted? 

^*     2— ?>    2+8  —  -    17  16'    1         16  —  16'     3—6'     36  —  - 

4.  What  kind  of  fractions  can  be  added  or  subtracted? 

5.  Express  |  as  sixteenths.  Add  |  and  -f^  ;  J  and  -f^  ;  | 
and  |. 

6.  Express  J  as  eighths.  Subtract  -|  and  | ;  J  and  -f^  ;  | 
and  Jg . 

133.  Two  or  more  fractions  whose  denominators  are  the  same 
are  said  to  have  a  common  denominator;  if  this  denominator 
is  the  smallest  possible,  the  fractions  are  said  to  have  a  least 
common  denominator.  Two  or  more  fractions  having  the  same 
denominator  are  sometimes  called  similar  fractions. 

ORAL  EXERCISE 

Change  to  similar  fractions  : 

1. 

2. 

3. 

4. 

5. 

WRITTEN  EXERCISE 

Change  to  fractions  having  the  least  common  denominator: 

^'  h   32'  H'  ^-  h  h    12'   Z2'  ^'  12'   9'  ¥'  i^* 

2-  f '  A'  2V  6.  |,  f ,  3^,  ^V  10.  iJ,  ^,  i  ^f . 

3.  h  h  I'  i-  7.  |,  -5^^,  ^2,  If  11.  ^Vo'  I'  I'e^'  f  • 
*•  I'   9'   iV  3-  S-  iV    A'  12'  }•  ^2-  61%  tV   3V'  ^2* 

Change  the  fractions  to  form  for  addition  or  subtraction: 

13.    31^,7^5.        14.    134Jj,112^.        15.   6126,^,178^. 


h\- 

6. 

-l-f 

11. 

f  f 

16. 

h  i>  i- 

hk- 

7. 

I'f- 

12. 

i  iV 

17. 

!'  r  \ 

h\- 

8. 

if 

13. 

iiV 

18. 

i'  i'  A- 

I'i- 

9. 

if 

14. 

I'tV 

19. 

i  h  f  • 

I'A- 

10. 

if 

15. 

iiV 

20. 

i'  1'  ^e- 

COMMON   FRACTIONS  107 


ADDITION 


134.     It  has   been  seen   that  only  like  numbers  and  parts  of 
like  units  can  he  added. 


0 

RAL  EXERCISE 

State  the  sum  of: 

1-  h  h  1- 

7,   2|,  3|,  12J,  19J. 

2-    i  1.  \- 

8.   5J,  121,  7^,  loj. 

3-    h   f   f 

9.    7J,  2|,  8i,  H,  2|. 

*•   ^v  ^-v  A- 

10.    2J,  5|,  8f  12J,  lOf. 

5-  i  i  f >  i  I- 

11.    IJ,  10|,  161,  181,  121. 

*•  iV'  iV  iV  i%- 

12.    5J.,  2-/5,  1^,  8^,  3f,. 

^^  horizontal  addition  find  the  sum  of : 

13.  2  pieces  of  gingham  containing  41^  and  43^  yd. 

In  the  dry-goods  business  fourths  (quarters)  are  very  common  fractions. 
They  are  usually  written  without  denominators  by  placing  the  numerators 
a  little  above  the  integers.  Thus,  51^  equals  51  J,  54^  equals  54|  (54|),  and 
523  equals  52|. 

14.  4  pc.  stripe  containing  A2\  38^  40^,  and  49  yd. 

15.  3  pc.  fancy  plaid  containing  42^,  40^,  and  41  yd. 

16.  4  pc.  duck  containing  48i,  47^,  46^,  and  40^  yd. 

17.  2  pc.  monument  cotton  containing  54^  and  55^  yd. 

18.  4  pc.  dress  silk  containing  32^,  342,  353^  and  322  yd. 

135.   Examples,     l.    Find  the  sum  of  |-  and  |. 

Solution,     |  and  |  are  not  similar  fractions  ;  1.  c.  m.  of  8  and  5  =  40 

hence,  make  them  similar  by  reducing  them  to  X=3-^*-2 16- 

equivalent  fractions  having  a  least  common  de-  35       1 6^^  5  1^     111 

nominator.      |  =  f^  and  |  =  i|.      H+H=H  40 +10  =  40  = -^57 

=  m- 

2.    Find  the  sum  of  m\,  34|,  52f . 

Solution.  By  inspection  determine  the  least  common  564  =  8 
denominator  of  the  given  fractions ;  then  make  the  frac-  0^1  __  3 
tions  similar  and  add  them,  as  shown  in  the  margin.        .^  . 

The  result  is  1 2^,  which  added  to  the  sum  of  the  into-  4    ~  _ 

gers  equals  143^,  the  required  result.  -^"^^  A      f  f  ~  -^  A* 

CB 


108  CONCISE   BUSINESS   ARITHMETIC 


WRITTEN  EXERCISE 


Find  the  sum  of: 

1-     ^6.1- 

7. 

12f,  172^. 

2-    .1^6'  II- 

8. 

8i  1.  \l  2Tf 

3.    2J,17J. 

9. 

52|,  591,  57|,  52^. 

4.   12|,19^. 

10. 

60|,  18|,  21,^5,  142jV. 

5.  m,in. 

11. 

204,  121,  18^,  92J,  75f. 

6.  21  4f ,  25J5. 

12. 

140f,  2601,  1451,  216J,  890| 

13.  A  carpet  dealer  sold  at  different  times  125|  yd.,  272 J 
yd.,  1691  yd.,  186f  yd.,  2411  yd.,  265|  yd.,  296|  yd.,  and 
314|-  yd.  of  Axminster  carpet,  at  $2.65  per  yard.  If  it  cost 
him  $2.45  per  yard,  what  was  his  gain? 

14.  A  dry-goods  merchant  bought  50  pc.  of  dress  silk  at 
$1  per  yard.  If  the  pieces  contained  42^,  432,  442,  473^  441^  452^ 
403,  462^  451^  42,  471,  482,  493^  491,  402,  403,  502,  493,  472,  483,  493^ 
451,  402,  452^  442^  473^  462^  411^  513^  423,  532^  572^  531^  511^  483,  472, 
401,  452,  452,  403,  401,  453,  472,  481,  511,  522,  572,  513,  502,  50i  yd., 
respectively,  and  he  sold  the  entire  purchase  at  $1.25  per  yard, 
what  was  his  gain  ? 

Short  Methods  in  Addition 

oral  exercise 

1.  1.  -f- 1  =  1|..  Observe  that  the  numerator  of  the  sum  is 
equal  to  the  sum  of  the  denominators  in  the  given  fractions. 

2.  ^  -{-  1  =  ?  Give  a  short  method  for  adding  any  two  sim- 
ple fractions  whose  numerators  are  1. 

3.  ^  -f- 1-  =  11^.  Observe  that  the  numerator  of  the  sum  is 
equal  to  the  sum  of  the  denominators  multiplied  by  the  numera- 
tor of  either  of  the  given  fractions. 

4.  I  +  I  =  ?  Give  a  short  method  for  adding  any  two  frac- 
tions whose  numerators  are  alike. 

5.  Find  the  sum  of  J,  \^  and  \' 

Solution,     i  +  i  =  1^2  ;  t^j  +  i  =  M)  the  required  result 


COMMON   FRACTIONS 


109 


ORAL  EXERCISE 


State  the  sum  of: 


1. 

h\' 

7. 

hh 

13. 

hh 

19. 

^^f 

2. 

h  h 

8. 

hh 

14. 

hh 

20. 

f  A- 

3. 

hh 

9. 

hh 

15. 

hh 

21. 

hhi 

4. 

hh 

10. 

hh 

16. 

hh 

22. 

hhi 

5. 

hi- 

11. 

hh 

17. 

h  h 

23. 

hh^ 

6. 

h  h 

12. 

hh 

18. 

hh 

24. 

hhi 

136.  The  most  common  business  fractions  are  usually  small 
and  of  such  a  nature  that  they  may  be  added  with  equally  as 
much  ease  as  integers.  The  following  exercise  will  be  found 
helpful  to  the  student  in  learning  to  add  these  fractions  in 
practically  the  same  manner  that  he  adds  integers. 

137.  Example.    Find  the  sum  of  -f^,  |,  |^  and  l. 

Solution.  By  inspection  determine  that  the  least  common  denominator  is 
16.  Then  mentally  reduce  each  fraction  to  16ths  and  add  as  in  whole  numbers. 
Thus,  5,  7, 19,  fl,  m. 


ORAL  EXERCISE 

Find  the 

sum  of: 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

* 

1 

i 

f 

i 

1 

i 

i 

1 

i 

f 

i 

i 

i 

i 

i 

f 

i 

i 

i 

* 

1 

6 

-^ 

i 

i 

* 

i 

i 

J 

i 

1 

i 

A 

i 

i 

i 

i 

1 

A 

1 

11. 

12. 

13. 

14. 

15. 

16. 

17. 

18. 

19. 

20. 

i 

* 

f 

i 

i 

1 

i 

J 

i 

i 

1 

1 

1 

f 

i 

i 

f 

i 

1 

i 

i 

1 

1 

t 

1 

1 

f 

i 

1 

J 

t 

i 

i 

i 

i 

i 

f 

2^ 

i 

4 

1 

^ 

1 

f 

i 

1 

i 

t 

i 

f 

i 

'^ 

tV 

f 

i 

f 

f 

f 

i 

1^ 

i 

A 

^ 

f 

1 

i\ 

1 

i 

i 

A 

i 

A 

^ 

i 

f 

iJ 

A 

* 

i 

^ 

110  CONCISE   BUSINESS   ARITHMETIC 

Exercises  similar  to  the  foregoing  should  be  continued  until  the  student 
can  name  the  successive  results  in  the  addition  without  hesitation. 

138.  The  ordinary  mixed  numbers  that  come  to  an  accountant 
should  be  arranged  for  addition  practically  the  same  as  in- 
tegers. In  adding,  the  fractions  should  be  combined  first  and 
then  the  integers. 

139.  Example.    Find  the  sum  of  2^  54,  and  3^. 

^ 

Solution.  By  inspection  determine  that  the  least  common  denomi-  ni 
nator  of  the  fractions  is  8.  Mentally  find  the  sum  of  the  fractions  and  ^ 
the  result  is  14.    Add  this  result  to  the  integers  and  the  entire  sum  is  114.  fi^ 


ORAL  EXERCISE 


State  the  sum  of , 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

2J 

H 

H 

H 

14i 

6| 

4i 

2| 

3^ 

14} 

?i 

2J 

H 

^ 

I7f    : 

13J 

'i 

16| 

iH 

16f 

11. 

12. 

13. 

14. 

15. 

16. 

17. 

18. 

19. 

20. 

9f 

^ 

n 

If 

8* 

4i 

5i 

H 

4* 

4J 

10^ 

4i 

^ 

6J 

S| 

2i 

2f 

5f 

2| 

If 

13i 

iij 

7^ 

6| 

2tV 

4i 

4i 

6f 

6t 

7f 

lOi 

12tV 

8A 

13| 

4t% 

3f 

6i 

2* 

3i% 

12J 

21. 

22. 

23. 

24. 

25. 

26. 

27. 

28. 

29. 

30. 

4J 

H 

^ 

H 

8i 

4| 

5| 

H 

4^ 

4^ 

5i 

6| 

^ 

If 

6| 

2^ 

IJ 

H 

2i 

H 

3| 

5f 

^ 

2f 

H 

4* 

n 

7f 

6f 

9| 

H 

5f 

7| 

6| 

2# 

3i 

^ 

5* 

6^ 

7| 

H 

^ 

li 

n 

4 

^ 

n 

2f 

9f 

8f 

4i 

^ 

2f 

2f 

5i 

H 

H 

n 

4i 

2J 

^ 

^ 

8iV 

8f 

2i 

H 

2f 

n 

3^ 

H 

H 

2i^ 

8A 

13f 

5,^ 

3i 

12J 

15f 

9t^ 

12J 

Exercises  similar  to  the  above  should  be  continued  until  the  student  can 
add  with  great  facility.  If  the  principles  of  grouping  have  not  been  well 
mastered,  simple  addition  should  be  carefully  reviewed. 


COMMON   FRACTIONS 


111 


WRITTEN  I 

SXERCISE 

Copy  i 

or  write  from 

dictation  and  find  the 

sum  of: 

1. 

2. 

3. 

4. 

5. 

6. 

1649J 

1672f 

14361 

21101 

6214J 

12141 

43721 

14851 

1390f 

16401 

1745J 

2167| 

8431| 

16351 

24151 

36801 

3146f 

31591 

5132J 

12641 

18671 

4590| 

18641 

9275J 

16541 

1269f 

16391 

2169f 

2839| 

7215f 

18311 

1748J 

4136f 

8432f 

6241J 

52611 

1831| 

1936| 

1652J 

40411 

4036| 

7215f 

14621 

54131 

31161 

6542f 

8130^ 

5144f 

1851^ 

2114jV 

1439^0 

18621 

2148^ 

6257f 

111^2 

8. 

2243/^ 
9. 

3246 1 
10. 

1439^^ 

2186^^2 

7. 

u. 

12. 

91241 

72491 

16491 

75291 

7365^ 

28141- 

2716^ 

2724| 

27241 

62141 

26141 

29101 

2514J 

86921 

86951 

18251 

15831 

2817i 

29671 

2476J 

15651 

8614| 

16951 

2714J 

2964J 

86951 

2724-1 

9215f 

17621 

2913| 

6875J 

62141 

86191 

6719f 

1875| 

2874f 

8875f 

72411 

2924f 

8516^ 

1629J 

26191 

26581 

86141 

65291 

75281 

7214| 

1472^ 

8425| 

4725^ 

85921 

7216| 

25101 

2615f 

8273| 

1649^ 

27251 

67291 

2625f 

1813| 

1782f 

12861 

8647| 

3514| 

8614J 

19621- 

8695^ 

6248| 

8725f 

1686f 

2729^ 

1862J 

24721 

12861 

6219| 

1725J 

28161 

1759J 

62731 

8537f 

84131 

2538f 

28141 

2864| 

9685f 

6982J 

7226f 

17581 

2716| 

1624J 

968511 

3685^ 

18251 

27521 

17621 

1729J 

1925-/2 

2614f 

4725-1 

21141 

18751 

1805| 

4212^2 

8796| 

2816| 

2216J 

2614| 

17211 

2729J^ 

1592| 

2519^ 

18721 

2075J 

1465| 

112 


COKCISE   BUSINESS   AEITHMETIO 


SUBTRACTION 


ORAL  EXERCISE 


1.  172  A.  -  154  A.  =  ?    |-f  =  ?     Ibu. -3pk.  =  ? 

2.  Find  the  difference  between  J  and  J  ;  ^  and  ^;  |  and  ^; 
f  and  f . 

140.  It  is  clear  that  onl^  like  numbers  and  parts  of  like  units 
can  he  subtracted. 

141.  Examples,     i.    Find  the  difference  between  J  and  -f^. 

Solution.  The  given  fractions  must  be  reduced  to  equivalent  fractions  having 
a  least  common  denominator.  The  least  common  denominator  is  24.  |  =  f|  and 
h  =  \l'    l\-\l  =  \h  ^^^  required  result. 

2.    From  211  take  171 

Solution.  Change  the  given  fractions  to  similar  fractions  as  in  example  1. 
^  cannot  be  subtracted  from  f ,  hence  1  is  taken  from  21  and  mentally  united 
to  I,  making  f.  |  from  |  leaves  |,  and  17  from  20  leaves  3,  The  required  result 
is  therefore  3|. 


ORAL  EXERCISE 

Find  the  value  of: 

1.    2|-J.                 5.   4f-l|. 

9. 

30- 

2.    2f-i.                  6.    6f-4^j. 

10. 

45- 

3.     31 -|.                        7.     1\~^-,. 

11. 

lli 

4.    7|-1|.                8.    12^-6^. 

12. 

70| 

16f. 
-61. 
-20J. 

The  following  is  a  recent  clipping  from  a  daily  paper.  It  shows  the 
prices  of  wheat  on  the  Chicago  market.  The  first  line  of  prices  is  for  wheat 
to  be  delivered  in  July,  and  the  second  line  for  wheat  to  be  delivered  in 
September. 

Chicago  Wheat  Quotations 


Delivery 

Previous  Closing 

Opening 

Highest 

Lowest 

Closing 

July 
September 

87f)^ 

90|^ 

881^ 

90f^ 
87)^ 

92^^ 
87|)^ 

13.  What  was  the  difference  between  the  highest  and  the 
lowest  price  of  July  wheat  ?  of  September  wheat  ? 

14.  What  was  the  difference  between  the  opening  and  the 
closing  price  of  September  wheat  ?   of  July  wheat  ? 


COMMON  FRACTIONS  113 

13.  What  was  the  difference  between  the  opening  price  and 
the  previous  closing  (yesterday's  closing)  price  of  July  wheat  ? 
of  September  wheat  ? 

16.  A  bought  1000  bu.  July  wheat  at  the  lowest  price  and 
sold  the  same  at  the  closing  price.     What  was  his  gain  ? 

Suggestion.     llf=  ^0.015 ;  1000  times  ^0.015  =  $ ? 

17.  B  bought  1000  bu.  September  wheat  at  the  opening 
price  and  sold  it  at  the  highest  price.  What  was  his  gain? 
Had  he  bought  at  the  lowest  price  and  sold  at  the  closing  price, 
what  would  have  been  his  gain  ? 

18.  C  bought  25,000  bu.  July  wheat  at  the  opening  price  and 
sold  it  at  the  highest  price.     What  was  his  gain  ? 

WRITTEN  EXERCISE 
Find  the  value  of: 

1.  39-111,  5.   I651-4I3V.  9.   l-i-i- 

2.  85-213.  6.   245f-17^g.  10.   i-^\-i. 

3.  168 -15f.  7.   177|-17fg.  11.   2i  +  lf-1^2- 

4.  264j9g_131i.        8.   2150- 121 1|.  12.   251 -8|- 151. 

142.  When  the  numerators  of  any  two  fractions  are  alike,  the 
subtraction  may  be  performed  as  in  the  following  examples. 

143.  Examples.     1.    From  |  take  l.     2.    From  |  take  f . 

Solutions.  1.  9  —  7=2,  the  new  numerator.  9  x  7  =  63,  the  new  denomi- 
nator. Therefore,  the  required  result  is  ^^.  2.  8  —  5  x  3  =  0,  the  new  numer- 
ator.    8  X  5  =  40,  the  new  denominator.     Therefore,  ^^  is  the  required  result. 


State  the  value  of: 

1-  J-J- 

8-    i-f 

15. 

*-f 

22. 

f-f 

2-    i-h 

9-    i-i- 

16. 

l-f 

23. 

J-f 

3-    J-J. 

10.   i-1. 

17. 

!-«• 

24. 

l-f- 

*•    i-h 

11.    i-1. 

18. 

l-f 

25. 

121 -6|. 

5-    i-h 

la.  l-f 

19. 

t-f 

26. 

13  J  -  21. 

6-    i-h 

13.   l-\. 

20. 

l-f 

27. 

^H-H- 

•>■    i-f 

14.     l-f 

21. 

f-i 

28. 

16f-12f, 

114  CONCISE   BUSINESS    AEITHMETIC 

MULTIPLICATION 

ORAL  EXERCISE 

1.  12  times  2  A.  are  how  many  acres?  12  times  2  fifths  (|) 
are  how  many  fifths  ?     ^^-  —  ? 

2.  32  mi.  divided  by  4  equals  how  many  miles?  \  of  32  mi. 
equals  how  many  miles?  Multiplying  by  ^,  ^,  ^,  and  |-,  etc.,  is 
the  same  as  dividing  by  what  integer  ? 

3.  If  5  men  can  dig  125  bu.  of  potatoes  in  1  da.,  how  many 
bushels  can  3  men  dig  in  the  same  time  ?  |  of  125  bu.  equals 
how  many  bushels  ? 

144.  Example.     Multiply  |  by  248. 

{a) 

Solutions,  (a)  248  times  3  eighths  =  744  eighths  |  x  248  =  -^4^=  93 
=  i|i  =  93;but, 

(6)  If  the  multiplication  is  indicated  as  in  the  "■*■ 

margin,  the  work  may  be  shortened  by  cancellation.  %^P  times  o  __  gg 

145.  Therefore,  to  find  the  product  of  an  integer  and  a 
fraction,  find  the  product  of  the  integer  and  the  numerator^  and 
divide  it  by  the  denominator. 

Before  actually  multiplying,  indicate  the  multiplication  and  cancel  if 


ORAL  EXERCISE 

1.  If  1  yd.  of  cloth  costs  87^/  (f|),  what  will  16  yd.  cost? 
48  yd.?  128  yd.?   72  yd.? 

2.  When  oats  cost  33i/  (fi)  a  bushel,  how  much  must  be 
paid  for  29  bu.?  for  36  bu.?  for  129  bu.? 

3.  A  boy  earns  75^  (S|)  a  day.  How  much  will  he  earn 
in  18  da.?  in  40  da.?  in  84  da.?  in  128  da.?  in  160  da.? 

4.  When  property  rents  for  $720  a  year,  what  is  the  rent 
for  J  yr.?  for  \  yr.?  for  \  yr.?  for  ^  jr.?  for  J  yr.? 

5.  A  ship  is  worth  $48,000.  What  is  |  of  the  ship 
worth  ?  ^g  of  the  ship  ?  |  of  the  ship  ?  ^  of  the  ship  ?  ^  of 
the  ship? 


COMMON   FRACTIONS  115 

WRITTEN  EXERCISE 

Find  the  product  of  : 

1.  98  X  |.  7.  J  of  95.  13.  784  x  f .  19.  f  of  2420. 

2.  80  X  f .  8.  f  of  25.  14.  459  x  \,  20.  |  of  2500. 

3.  50  X  2V  9-  I  of  88.  15.  400  X  iV  21.  I  of  3240. 

4.  97  X  ^,  10.  ^9g  of  51.  16.  510  X  iV  22.  f  of  5117. 

5.  92xiV  11.  2^0^99.  17.  990  XsV  23.  ^  of  7254. 

6.  188  X  6^1.  12.  -j^g  of  77.  18.  800  x  if.  24.  ^  of  1024. 

146.    Example.     MultiDly  25  by  4|. 

25 
Solution.      |  of  25  =  ^{-  or  9|.     Write  f  as  shown  in  the  margin, 


and  carry  9  to  the  product  of  the  integers.     4  x  25  +  9  =  109.    There- 
fore, 25  multiplied  by  4f  =  109|.  109| 

147.  Therefore,  to  find  the  product  of  a  mixed  number 
and  a  whole  number,  multiply  the  integer  and  the  fraction  sepor 
rately  and  find  the  sum  of  the  products, 

ORAL    EXERCISE 

Find  the  cost  of: 

1.  15f  lb.  of  fish  at  9^.  6.  6|  bu.  turnips  at  32^. 

2.  7f  yd.  of  cloth  at  83.  7.  12 J  bu.  of  oats  at  39^. 

3.  16  lb.  of  beef  at  12 1  ^.  8.  l^  yd.  of  calico  at  4^. 

4.  l^  lb.  of  sugar  at  5^.  9.  ^^  yd.  of  ribbon  at  20 )Z^. 

5.  12  yd.  of  cloth  at  11^^.  10.  8J- gal.  of  molasses  at  40^. 

WRITTEN   EXERCISE 

1.  A  merchant  bought  24  pc.  of  English  serge,  containing  52, 
472,  501,  483,- 49,  513,  47^  482^  453^  491^  522,  502,  51^,  50,  52,  53i, 
523,  473^  481,  512,  513^  482,  49,  and  53  yd.,  at  $1,121  per  yard,  and 
sold  it  all  at  S1.35  per  yard.     What  did  he  gain  ? 

2.  I  bought  25  pc.  taffeta  silk,  contaming  42^,  40^,  43,  44^ 

45,  412,  43^  461^  472^  44^  452^  491^  471^  451^  46^  44^  433^  40,  41^, 

46,  47,  402,  451,  42,  and  47^  yd.,  at  871/  per  yard,  and  sold 
the  first  15  pc.  at  S1.05  and  the  remainder  at  Sl.lO.  What 
did  I  gain? 


116 


CONCISE   BUSINESS   ARITHMETIC 


3.  A  merchant  bought  25  pc.  of  striped  denim  containing 
411,  411,  422^  432^  421,  442^  431^  402^  421,  453^  42i,  402,  412,  473^ 
451,  411,  432^  472^  443^  423,  432,  391,  421,  482,  and  47  yd.,  at  11/ 
per  yard.  If  he  sold  the  first  11  pc.  at  15/  per  yard  and  the 
remainder  at  17/  per  yard,  what  was  his  gain? 

4.  Copy  and  find  the  amount  of  the  following  bill : 

Little  Falls,  NV.,  {U^^-^^^'r^       tq 


Te..s  ^^^^^/"^^^  ^'  The  Eureka  Mills 


^ 


A-X-r^-p^^-^^-^^y-^f^.^i^^^r:^^ 


l.^^'^J'T^^ 


AC/'   AC2/    A^jT'    4^/7      4^/ 2.//^Uc^.      S^%<\ 


r  \J2^^  ~:^7^^i^^.,^^^:^^^-/>r^  ..^i^^^^^^^ 


^2.'  AC/    .ic7-'    ^^"^  A^2. dZZ. 


LO. 


^^'^^^T'^^ 


4^/     Jf 4^ 4L/. A^O 


-%i 


148.  The  expressions  |^  of  |^  and  ^  X  f  have  the  same  meaning ; 
hence  the  sign  of  multiplication  may  be  read  of,  or  multiplied  hy^ 
when  it  immediately  follows  a  fraction. 

149.  Examples.     1.    Multiply  |  by  |. 

Solution.     To  multiply  f  by  |  is  to  find  f  of  f . 

Let  the  line  ^JF  in  the  accompanying  diagram  represent  a  unit  divided  into 
5  equal  parts.  ad  p  n  f  T7 

Then  ^D  will  represent  |.     Sub-     ^  ^  C  D  E  F 

divide  each  of  the  five  equal  parts 
into  3  equal  parts  and  the  line  AF 
will  represent  a  unit  divided  into  15 
equal  parts,  each  of  which  is  -^^  of  the  whole.  It  is  then  clear  that  y  of  ^ 
equals  ^^.  Since  |  of  ^  is  J^,  ^  of  f  is  ^^.  But  |  of  f  is  2  times  |  of  f ;  there- 
fore f  of  I  equals  y^. 

2.    Find  the  product  of  2i,  |,  and  -^j. 

Solution.     Reduce  the  mixed  number  2\  to  an  im-  2 

proper  fraction  and  obtain  ^.     Cancel,  and  there  remains  5      4       7       14 

in  the  numerators  2  times  7,  and  in  the  denominators  15,  Tj^'g.^  Tc  ~  i~c 

from  which  obtain  the  fraction  \^.  r      r 


COMMON   FRACTIONS 


117 


150.    Hence,  to  multiply  a  fraction  by  a  fraction ; 

Reduce  the  mixed  numbers  and  integers  to  improper  fractions 
and  cancel  all  factors  common  to  the  numerators  and  denominators. 

Find  the  product  of  the  remaining  numerators  for  the  required 
numerator^  and  the  product  of  the  remaining  denominators  for  the 
required  denominator, 

ORAL  EXERCISE 

1.  How  many  yards  in  |  rd.  ?    feet  in  |  rd.  ? 

2.  When  barley  is  worth  25^^  per  bushel,  what  is  the  value 
of  Ibu.?     of  |bu.? 

3.  A  book,  the  retail  price  of  which  was  $5,  was  sold  at 
wholesale  for  ^  of  the  retail  price,  with  ^^  off  from  that  for 
cash.     Find  the  selling  price  of  10  books. 

WRITTEN   EXERCISE 
Reduce  to  their  simplest  form  : 

1.  I  of  I  off  3.    7^x25xf.  5.    50x^xT|. 

2.  fof|of2J.  4.    3fx  41x20.  6.    l|x4J-x8f. 

7.  A  saves  89.75  per  week  and  B  |  as  much.  How  much 
more  will  A  have  than  B  at  the  end  of  a  year  ? 

8.  A  merchant  bought  a  piece  of  cloth  containing  43|^  yd. 
at  $1.50  per  yard.  He  sold  |  of  it  at  f  1.62 J  a  yard,  and  the  re- 
mainder at  f  1.37 J  a  yard.     Did  he  gain  or  lose,  and  how  much? 

The  following  is  a  recent  clipping  from  a  daily  paper.  It  shows  the 
prices  of  corn  on  the  New  York  market. 


New  York  Corn  Quotations 


Delivery 

Previous  Closing 

Opening 

Highest 

Lowest 

Closing 

July 
September 

661/ 
651/ 

65|/ 
64J/ 

661/ 
65^/ 

64J/ 
641/ 

65|/ 
64f/ 

9.  D  bought  25,000  bu.  September  corn  at  the  opening 
price  and  sold  it  at  the  highest  price.  What  was  his  gain? 
Had  he  bought  at  the  lowest  price  and  sold  at  the  highest 
price,  what  would  he  have  gained? 


118  CONCISE   BUSIKESS  ARITHMETIC 

10.  E  bought  12,500  bu.  July  corn  at  the  lowest  price  and 
sold  it  at  the  closing  price.  What  was  his  gain  ?  Had  he 
bought  at  the  lowest  price  and  sold  at  the  highest  price,  what 
would  he  have  gained? 

11.  A  gold  dollar  weighs  25.8  troy  grains.  For  every  90 
parts  of  pure  gold  there  are  ten  parts  of  alloy.  How  many 
grains  of  each  kind  in  a  gold  dollar  ?  in  a  5-dollar  gold  piece  ? 

12.  A  5-cent  piece  weighs  77.16  troy  grains.  For  every 
part  of  nickel  there  are  three  parts  of  copper.  How  many 
grains  of  each  kind  in  a  5-cent  piece  ? 

13.  The  second  general  coinage  act  (1834)  of  the  United 
States  made  one  silver  dollar  weigh  approximately  as  much  as 
sixteen  gold  dollars,  and  this  ratio  of  sixteen  to  one  has  been 
maintained  up  to  the  present  time.  What  is  the  approximate 
weight  of  a  silver  dollar  ?  If  silver  coins  are  -f^  pure,  approxi- 
mately how  much  pure  silver  in  10  silver  dollars? 

Short  Methods  in  Multiplication 

151.  When  mixed  numbers  are  large,  they  maybe  multiplied 
as  shown  in  the  following  example. 

152.  Example.     Multiply  2551  by  24f. 

2551 

Solution.    Multiply  the  fractions  together  24I 

and  obtain  ^5,  which  write  as  shown  in  the        ^^   2     -  - 

margin.    Multiply  the  integer  in  the  multi-  T^  ~  5"        3 

plicand  by  the  fraction  in  the  multiplier  and  102       =  |^  of  265 

obtain  102.    Multiply  the  fraction  in  the  mul-  8       =24  times  ^ 

tiplicand  by  the  integer  in  the  multiplier  and  1020  1 

obtain  8.     Multiply  the  integers  together  and  tj     i    =  24  times  255 

add  the   partial   products.      The   result   is  ^                                

6230^.  6230^2^  =  24f  times  255J 

WRITTEN  EXERCISE 

Multiply  : 

1.  975Jbyl8J.  3.    720Jby21|.  5.    512^  by  161. 

2.  876|by21|.  4.    445iby46|.  6.   450^^  by  20|. 


COMMON  FRACTIONS  119 

SQUARING  NUMBERS   ENDING  IN   J  OR  .5 

153.    Examples,     i.    Multiply  9J  by  9i. 

Solution.     |  of  ^  =  J,  which  write  as  shown  in  the  margin.    ^  9i 

of  the  integer  in  the  multiplicand  plus  ^  of  the  integer  in  the  multi-  qj^ 

plier  is  equal  to  either  the  integer  in  the  multiplicand  or  multiplier.  -— | 

Therefore,  add  1  to  the  integer  in  the  multiplicand  and  multiply  by  the  5 
multiplier.    9  x  10  =  90.     Then,  9^  x  9J  =  901. 

2.  Find  the  cost  of  8.5  T.  of  coal  at  18.50  per  ton. 

Solution.  The  principles  embodied  in  this  example  are  practi- 
cally the  same  as  those  in  problem  1.  .5  x  .5  =  .25,  8  x  9  =  72. 
Therefore,  8. 5  tons  of  coal  at  § 8.50  per  ton  will  cost  $ 72.25.  72.25 

3.  Find  the  cost  of  75  A.  of  land  at  $75  per  acre. 

Solution.    This  problem  is  similar  to  example  2,    the  only  75 

difference  being  in  the  matter  of  the  decimal  point.     Since  the  ne 


8.5 
8.5 


5625 


decimal  point  has  no  particular  bearing  upon  the  steps  in  the  pro- 
cess of  multiplying,  proceed  to  find  the  product  as  in  example  2. 
5  X  5  =  25,  which  write  as  shown  in  the  margin.    7  x  8  =  56,  which  write  to  com- 
plete the  product.    75  acres  of  land  at  $75  an  acre  will  therefore  cost  $5625. 


ORAL  EXERCISE 

Multiply : 

1.  11  by  11  6.  6 J  by  61    ii.  131  by  ISJ.  16.  161  by  161. 

2.  21  by  21  7.  7.5  by  7.5.  12.  141  by  141.  17.  171  by  171. 

3.  31  by  31.  8.  8.5  by  8.5.  13.  151  by  151  is.  18 J  by  18^. 

4.  4^  by  41  9.  9.5  by  9.5.  14.  11.5  by  11.5.  19.  195  by  195. 

5.  51  by  51.  10.  10.5  by  10.5. 15.  12.5  by  12.5.  20.  205  by  205. 

WRITTEN  EXERCISE 

In  the  following  problems  make  all  the  extensions  mentally, 

1.    Find  the  total  cost  of: 

85  lb.  of  tea  at  85  f.  55  lb.  tea  at  55  ^. 

75  gal.  sirup  at  75^.  75  bbl.  flour  at  17.50. 

45  gal.  sirup  at  45^.  650  bbl.  oatmeal  at  $6.50. 

2|  bu.  beans  at  $2.50.  25  doz.  cans  olives  at  $2.50. 

35  gal.  molasses  at  35^.  95  cs.  salad  dressing  at  95^. 

65  cs.  horseradish  at  Qtb^,  750  lb.  cream  codfish  at  7J^. 

4 J  cs.  baking  powder  at  $  4.50.  3 J  cs.  baking  powder  at  $  3.50. 


120  CONCISE   BUSINESS   ARITHMETIC 


MULTIPLICATION   OF   ANY  NUMBERS   ENDING   IN  |^  OR    .5 

154.    Examples,     l.   Multiply  7^  by  6|. 

Solution.    |  of  the  integer  in  the  multiplicand  plus  ^  of  the  integer  gl 

in  the  multiplier  is  equal  to  ^  of  6  +  7,  or  0^,  which  added  to  ^  of  ^  r-l 

equals  6|.     Write  f  as  shown  in  the  margin,  and  carry  6.     6x7+  6  j-^ 

=  48.    Therefore,  7|  x  6|  =  48|.  ^^f 

2.    Multiply  7i  by  9J. 

7J- 

Solution.     |  of  7  +  9  =  8,  with  no  remainder.     ^  of  |  =  ^,  which  ^^ 

write  as  shown  in  the  margin,  and  carry  8.      7x9  +  8  =  71.     There-  2 

fore,  7^  X  9|  =  71|.  71^ 

Observe  that  :  (1)  in  finding  -|  of  any  number  (dividing  a  number  by  2) 
there  is  either  nothing  remaining  or  1  remaining ;  (2)  in  finding  |  of  an 
even  number  there  can  be  no  remainder,  and  in  finding  ^  of  an  odd  number 
there  is  always  a  remainder  1.    Hence,  to  multiply  numbers  ending  in  ^  or  .5 : 

Mentally  determine  the  sum  of  the  integers  in  the  multiplicand  and  multiplier. 
If  it  is  an  even  number,  write  \  {.25  or  25)  in  the  product.  If  it  is  an  odd  num- 
ber^ write  f  {.75  or  75)  in  the  product.  Multiply  the  integers  and  to  the  product 
add  \  of  their  sum. 


Multiple/ : 

ORAL  EXERCISE 

1-    3|by7i. 

2.  4|by6J. 

3.  16Jby4^. 

4.  17Jby2J. 

5.  141  by  61 

6.  21Jby9J. 

7.  3.5  by  8.5, 

8.  7.5  by  6.5, 

9.  5.6  by  8.5, 

WRITTEN  EXERCISE 

Make  the  extensions  in  each  of  the  following  problems  mentally, 

1,  Find  the  total  cost  of  : 

6.5  T.  coal  at  $8.50.  8.5  T.  coal  at  $9.50. 

2.5  T.  hay  at  $17.50.  16.5  T.  hay  at  $11.50. 

15.5  cd.  wood  at  $3.50.  14.5  cd.  wood  at  $5.50. 

2.  Find  the  total  cost  of  : 

45  bu.  beans  at  $2.50.  350  bu.  wheat  at  $1.05. 

35  bbl.  flour  at  $6.50.  350  bu.  beans  at  $2.50. 

45  bbl.  flour  at  $8.50.  85  bbl.  oatmeal  at  $7.50. 


COMMON  FRACTIONS  121 


DIVISION 


ORAL  EXERCISE 


1.  8A. -4-4  =  ?     Sninths  (|)-f-4? 

2.  If  2  lb.  of  cofPee  costs  |0.66|  (If),  what  will  1  lb.  cost? 
Divide  |  by  2.  What  is  the  effect  of  dividing  the  numerator 
of  a  fraction  ? 

3.  i  +  2  =  ?     Joft=? 

4.  Because  ^-h2  =  ^  of  |,  therefore,  |  -=-  5  =  ^  of  ^,  or 
ixi.     ixi  =  ? 

5.  What  is  the  quotient  of  1 -5- 5 ?     of-|-^8?     ofi-T-2? 

6.  Because  |-  -f-  5  =  ^  of  J,  therefore  |  -f-  5  =  2  times  J  of  ^. 
That  is,  f  ^  5  =  I  of  |,  or  I  X  f     |  x  l  =  ? 

7.  How  much  is  1^5?     f-3?     7l(-Y.)^8?     31^6? 

8.  What  is  the  effect  of  multiplying  the  denominator  of  a 
fraction  ? 

155.  In  the  above  exercise  it  is  clear  that 

Dividing  the  numerator  of  a  fraction  hy  an  integer  divides  the 
whole  fraction  ;  and, 

Multiplying  the  denominator  of  a  fraction  by  an  integer  divides 
the  whole  fraction, 

ORAL  EXERCISE 

Find  the  quotient  of: 

1.  f-r-4.       4.   |-^12.  7.  ■35^-^4.  10.   f-f-9.  13.  1-^19. 

2.  j%-Sr2.     5.   f-^12.  8.  iV^^-  ^^-   i-^^'  ^*-  A"^^- 
3.1^^5.       6.    ^9_^3.  9.  -A  ^7.  12.^^5.  15.  ^V^  5- 

156.  Examples.     1.    Divide  28J  by  7. 

Solution.    First  divide  the  integers  and  the  result  is  4 ;    then  44 

divide    the    fraction    by     7  and     the    result    is    |.        Therefore,      7\OQ,7 
28|-7  =  4f  ^      8 

2.   Divide  261  by  8. 

Solution.    Divide  26  by  8  and  the  result  is  3  with  a  remainder  2.  3_5_ 

Join  the  remainder,  2,  with  the  fraction,  |,  making  2^.     Reduce  2|  ONOfiT" 

to  an  improper  fraction  and  the  result  is  f .    f  -^  8  =  ^^.    Therefore,  ^      2 
20^  -  8  =  3^. 


122  CONCISE   BUSINESS   ARITHMETIC 

ORAL  EXERCISE 

Divide : 

1.  161  by  4.  5.  32f  by  4.  9.  21^  by  8.  13.  8^  by  5. 

2.  18|  by  9.  6.  271  by  7.  lo.  24^  by  6.  14.  14f  by  7. 

3.  25|  by  2.  7.  19|  by  9.  ii.  45f  by  5.  15.  Ill  by  9. 

4.  171  by  8.  8.  20f  by  10.  12.  40|  by  10.  16.  261  by  10. 

ORAL  EXERCISE 

1.  How  many  eighths  in  one  ?     1  -*- 1  =  ? 

2.  What  is  the  value  of:  Ih-J^?  ^--1?  11-^1? 
125-^^2?     250-^? 

3.  Read  aloud  the  following,  supplying  the  missing  word: 
To  divide  an  integer  hy  a  unit  fraction^  multiply  the  integer  by 
the of  the  fraction. 

4.  What  is  the  value  of  25 -i- 1  ?  2.5-^1?  7.5^  |?  25.5^ 
_L?  54^1?  48^1?  29^-1?  21^1? 

5.  If  B^  in  the  accompanying  dia- 
grahi,  is  1,  what  is  (7?  How  many 
blocks  like  OinBl   1  h- i  =  ? 

6.  If  A  is  1,  what  is  ^  ?  J.  is  how 
many  times  B ?  That  is,  A^B=? 
1-4-1  =  ? 

7.  If  1^1  =  1(11),  then  2-1  =  ? 

8.  What  is  the  value  of  4 -J- f  ?   5-4-|?     12-4-|?   15-4-f? 

9.  Read  aloud  the  following,  supplying  the  missing  words  : 

If  JL  is  1,  -S  is ,  and  C  is .      If  B  is   contained  in 

-4  I  (1  J)  times,  it  is  contained  in  (7  l  of  |  times  or times. 

That  is,  i-5-|  =  J  X  I  = . 

10.    What  is  the  value  of  1-^^?     fH-|?     f-^f?    f^f? 

157.  The  reciprocal  of  a  fraction  is  1  divided  by  that  fraction. 
Thus,  the  reciprocal  of  |  is  1  -,- 1,  or  |.    That  is,  the  reciprocal  of  a  fraction 

is  the  fraction  inverted. 

158.  Reciprocal  numbers,  as  we  use  the  terms  in  arithmetic, 
are  numbers  whose  product  is  1. 

Thus,  4  and  \,  %  and  |,  \  and  6,  |  and  |,  are  reciprocal  numbers,  because 
their  product  is  equal  to  1. 


COMMON  FRACTIONS 


123 


159.  It  has  been  seen  that  the  brief  method  for  dividing  a 
fraction  or  an  integer  by  a  fraction  is  to  multiply  the  dividend 
hy  the  reciprocal  of  the  divisor. 

The  principles  of  cancellation  should  be  used  whenever  possible.  Inte- 
gers and  mixed  numbers  should  be  reduced  to  improper  fractions  before 
applying  the  rule.  » 


Divide , 


WRITTEN  EXERCISE 


7. 

fbyf. 

8. 

4f  by  f . 

9. 

^by|. 

LO. 

6|  by  11 

1-  ibyf. 

2.  7|byi. 

3.  95  by  f . 

4.  88byf. 

5.  16by|.  11.    160  by  41 

6.  151  by  f  12.    250  by  3f . 

.    160.   Examples,     i.    Divide  2190  by  48|. 

Solution.  Multiplying  both  dividend  and  divisor  by 
the  same  number  does  not  affect  the  quotient;  hence,, 
multiply  the  dividend  and  divisor  by  3  and  obtain  for  the 
new  dividend  and  divisor  6570  and  146,  respectively. 
Divide  the  same  as  in  simple  numbers  and  obtain  the 
result  45.     Or, 

Reduce  both  the  dividend  and  divisor  to  thirds,  obtain- 
ing ^^a  and  i|6..  Reject  the  common  denominators 
and  divide  as  in  whole  numbers. 

2.    Divide  Q^  by  12J. 

Solution.  Multiply  both  dividend  and  divisor  by  6, 
the  least  common  denominator  of  the  fractions,  and  di- 
vide as  in  simple  numbers.     The  result  is  5^|.     Or, 

Reduce  both  the  dividend  and  divisor  to  sixths,  obtain- 
ing as  a  result  ^  and  ^.  Reject  the  common  denomi- 
nator and  divide  as  in  simple  numbers. 


Divide: 

1.  2701  by  121 

2.  508iby30|. 

3.  1431^  by  201. 

CB 


WRITTEN  EXERCISE 


13. 
14. 
15. 
16. 
17. 
18. 


ibyf 
fbyf 
169  by  4|. 
640  by  5|. 
625  by  831 
920f  by  73. 


48f)2190 

_3 3_ 

146)  6570(45 
584 
730 
730 


121)651 

_6 6_ 

74)393(5fi 

370 

23 


9621  by  31J. 
650f  by  261 
1680J  by  451. 


7.  7552by78f. 

8.  470|byl7|. 

9.  10541  by  168f 


124  CONCISE   BUSINESS   ARITHMETIC 

FRACTIONAL  RELATIONS 

ORAL  EXERCISE 

^^  1.    If  /  in  the  accompanying  diagram  is 

^^2  1,  what  is  e?    d?    c?   b?  a? 

^^L  2.    What  part  of  e  is /?    aid?    oi  c?    of 

^^b^  h?    of  a?    What  part  of  6  is  1?    of  5?   of  4  ? 

^^B^j^  '      3.    What  part  of  a  is  e?    d?    c?    b?    What 
^•^  part  of  6  is  2?    3?    4?    5? 

4.  What  part  of  d  is/?  What  part  of  5  is  e?  What  part 
of  1  (f )  is  I  ?     What  part  of  f  is  1  (|)  ? 

5.  What  part  of  7  bu.  is  1  bu.?  What  part  of  7  eighths  (|) 
is  1  eighth  (J)? 

6.  What  part  of  |  is  ^? 

Solution,  f  and  |  are  similar  fractions ;  hence  they  may  be  compared  in 
the  same  manner  as  concrete  integral  numbers.  2  is  |  of  3 ;  therefore,  |  is  |  of 
f ;  or, 

f  is  I  off.    |  =  fxf  =  f. 

7.  f  is  what  part  of  If  (|)  ?    of  2|?    of  5^? 

8.  ^  is  what  part  of  ^  ?       ' 

Solution.    ^  =  f .     |  is  ^  of  f ,  therefore,  |  =  J  of  ^ ;  or, 

iisiofi.  i=ix^=i. 

161.  To  find  what  fraction  one  number  is  of  another,  take  the 
number  denoting  a  part  for  the  numerator  of  the  fraction,  and  the 
number  denoting  the  whole  for  the  denominator. 

ORAL  EXERCISE 

1.  If  a  piece  of  work  can  be  performed  in  12  da.,  what 
part  of  it  can  be  performed  in  5  da.  ?  in  7  da.  ? 

2.  If  A  can  do  a  piece  of  work  in  15  da.,  what  part  of  it 
can  he  do  in  1  da.  ?  in  2  da.  ?  in  5  da.  ?  in  7|  da.  ? 

3.  If  B  can  do  a  piece  of  work  in  1^  da.,  what  part  of  it 
can  he  do  in  1  da.  ?  in  2  da.  ?  in  6  da.  ?  in  5 J  da.  ?  in  6 J  da.  ? 


COMMOK  FEACTIONS  125 

4.  What  part  of  100  is  331?  I2i  ?  6Gf  ?  8i  ?  25?  75? 
125?  16f?  831?  G2|-?  22|  ?  9^^-?  56 ^  ?  6f? 

5.  What  part  of  SI  is  331/?  66|/?  25/?  75/?  16f/? 
81/?  6f/?  31/?  6|/?  62^/?  871/?  371/?  142/? 

6.  What  part  of  1000  is  125?  166|?  666f  ?  625?  3331? 

7.  Whatpartof  S10isS3.331?  S1.25?  $1.66|?  S8.33i? 
$2.50?  $6.25?  $6.66f  ? 

WRITTEN   EXERCISE 

1.  A  man  asked  for  a  horse  |  more  than  it  cost,  but  finally 
reduced  the  price  -J^^.  He  gained  $  26.  What  was  the  cost  of 
the  horse  ?    the  price  asked  ?    the  selling  price  ? 

2.  A  had  1  of  his  money  invested  in  bonds,  -f^  in  bank  stock, 
and  the  remainder,  81980,  on  deposit  in  the  First  National  Bank. 
How  much  was  invested  in  bonds  ?    in  bank  stock  ? 

3.  A  man  left  his  estate  to  his-  four  sons.  To  the  first  son  he 
gave  1  of  the  estate ;  to  the  second,  1  of  the  remainder ;  to  the 
third,  ^  of  the  estate ;  to  the  fourth  son,  $1556.  What  was  the 
value  of  the  estate  ? 

4.  A  merchant  reduced  the  marked  price  of  a  machine  1,  and 
then  sold  it  so  that  he  gained  ^  of  the  first  cost.  If  he  gained 
$  8,  what  was  the  first  cost  of  the  machine,  and  the  marked  price 
before  any  reduction  was  made  ? 

5.  A  man  placed  a  house  and  lot  in  the  hands  of  a  real  estate 
agent  to  be  sold  at  such  a  price  that  he,  the  owner,  might  realize 
$5985,  after  paying  the  agent  2V  of  the  selling  price  of  the 
property.     For  how  much  was  the  property  sold? 

6.  A  farmer  had  three  bins  containing  wheat,  rye,  and  oats 
respectively.  The  quantity  of  oats  was  three  times  that  of  the 
wheat,  and  the  rye  was  one  haK  of  the  quantity  of  the  oats.  If 
the  value  of  the  oats  at  35/  per  bushel  was  $1155,  how  many 
bushels  of  each  kind  of  grain  did  the  farmer  have  ?  If  the 
wheat  was  worth  95/  per  bushel,  and  the  rye  67^/  per  bushel, 
what  was  the  value  of  the  entire  lot  of  grain  ? 


126  CONCISE   BUSINESS   ARITHMETIC 


WRITTEN   EXERCISE 

1.  The  square  in  the  margin  represents  the 
total  population  of  the  state  of  New  York  (state 
census  of  1910),  and  the  shaded  area  represents 
the  urban  (city)  population.  If  the  rural  (coun- 
try) population  is  1,800,000,  what  is  the  entire 
population  of  the  state  ?  the  urban  population  ? 

2.  In  a  recent  year  the  population  of  Massachusetts  was  in 
round  numbers  3,360,000,  and  there  were  fourteen  persons  living 
in  the  cities  of  the  state  to  each  person  living  in  the  country. 
Represent  this  graphically  as  in  problem  1,  and  find  the  city 
population  and  the  country  population  for  the  state. 

A 
B 

c 

D 
E 
F 


1 1 1 r 

12  3  4 


3.  Suppose  that  0  in  the  diagram  represents  the  population 
of  the  United  States  in  1870,  A  the  population  in  1830,  and  F 
the  population  in  1900.  If  the  population  in  1870  was  38,400,000 
(round  numbers),  what  was  the  population  (round  numbers) 
in  1900?     In  1830? 

4.  Suppose  that  F  in  the  diagram  represents  the  population 
of  the  United  States  in  1900,  and  O  the  proportion  of  this  popula- 
tion living  in  cities  in  1900.  What  proportion  of  the  popula- 
tion lived  in  cities  in  1900?  Suppose  that  F  represents  the 
population  in  1860  and  A  the  proportion  of  this  population 
living  in  cities.  Assuming  that  the  city  population  in  1860 
was  5,240,554,  find  the  total  population  for  the  same  year. 

5.  The  total  population  of  New  Jersey  (state  census  of  1910) 
is  2,537,167,  and  the  rural  population,  629,957.  Represent  this 
.graphically  and  find  the  urban  population. 


COMMON  FEACTIOKS  127 


CONVERSIOK   OF  FRACTIONS 

ORAL  EXERCISE 

1.  What  is  the  denominator  of  the  decimal  .6?  of  .75? 

2.  What  is  the  numerator  of  .4?  of  .04?  of  .004?  of  .0004? 

3.  Write  as  a  common  fraction  .7;  .23;  .079;  .0013;  .00123. 

162.  A  decimal  may  be  written  as  a  common  fraction. 

163.  Examples,     l.   Reduce  .0625  to  a  common  fraction. 

SoLUTiox.     .0625  means  yf  ^  ;  but  yf  §f^  may  be  625     ^^   5   _  J 

expressed  in  simpler  form.    Dividing  both  terms  of  T0^0()¥       So       1^ 

the  fraction  by  625,  the  result  is  ^. 

WRITTEN  EXERCISE 

Reduce  to  a  common  fraction  or  to  a  mixed  number: 

1.  0.375.  5.   0.9375.  9.   0.0335.  13.  260.675. 

2.  0.0625.         6.   1.66f.  10.   0.00561  14.  126.1875. 

3.  0.0016.         7.   0.4375.         ii.   181.875.         15.  175.0625. 

4.  0.5625.        8.   0.125.  12.   171.245.         16.  172.0075. 

164.  A  common  fraction  may  be  written  as  a  decimal. 

165.  Example.    Reduce  f  to  a  decimal. 

Solution,     f  equals  i  of  3  units.     3  units  equals  3000  thou-  *"'^ 

sandths.     \  of  3000  thousands  equals  375  thousandths  (.375).  8)3.000 

ORAL  EXERCISE 

1.  Reduce  to  equivalent  decimals :  J,  ^,  |,  \,  |,  J,  f ,  i,  |,  |, 

13     5     7    JL    _i .3-    1    JL 

1^'  ^'  ^'  t'    16'   12'    16'    9'    11- 

2.  Reduce  to  common  fractions  :  .5,  .25,  .50,  .75,  .331,  .66|, 
.16f,  .121  .6,  .4,  .60,  .40,  .2,  .831-,  .20,  .08J,  .375,  .125,  .371 
.87f  .875,  .0625,  .111  m^. 

WRITTEN  EXERCISE 

Reduce  to  equivalent  decimals : 

1.  f         3.    ^j.         5.    ^j.       7.    :^\.        9.    ^^.      11.    21f. 

2.  ^.       4.    I'j.         6.    ii  8.    2V.        10.    6,^.         12.    165^. 


128  CONCISE   BUSINESS   ARITHMETIC 

THE   SOLUTION  OF  PROBLEMS 

166.  The  steps  in  the  solution  of  a  problem  are  :  (1)  reading 
the  problem  to  find  what  is  given  and  what  is  required;  (2)  de- 
termining from  what  is  given  how  to  find  what  is  required; 

(3)  outlining  a  process  of  computation  and  then  performing  it; 

(4)  checking  results. 

167.  A  problem  should  be  thoroughly  understood  before  any 
attempt  is  made  to  solve  it ;  and  when  the  relation  of  what  is 
given  to  what  is  required  has  been  discovered,  the  process  of 
computation  should  be  briefly  indicated  and  then  performed 
as  briefly  and  rapidly  as  possible. 

168.  To  insure  accuracy  the  work  should  always  be  checked 
in  some  manner.  If  the  answer  to  the  problem  is  estimated  in 
advance,  it  will  prove  an  excellent  check  against  absurd  results. 

Thus,  42  doz.  boys'  hose  at  $48  a  dozen  is  equal  to  approximately 
40  X  $50 ;  9f  %  of  1290  bu.  is  equal  to  approximately  ^V  of  1290  bu. ;  etc. 

169.  Example.    A  tailor  used  30  yd.  of  flannel  in  making  18 

waistcoats  ;  at  that  rate  how  many  yards  will  he  require  in 

making  45  waistcoats  ? 

Solution 

1.  The  quantity  needed  in  making  18  waistcoats  is  given  and  the  quantity 
needed  in  making  45  waistcoats  is  required. 

2.  One  waistcoat  requires  f  f  yd. ;  45  waistcoats  will  require  45  times  f f  yd. 
15  5 

3.   r^ =  75 ;  that  is  75  yd.  of  flannel  are  required  in  making  45 

waistcoats. 

4.  1^  yd.  =  f  yd.  ;  ||  yd.  =  |  yd. ;  therefore  the  work  is  probably  correct. 

170.  If  reasons  for  conclusions,  processes,  and  results  are  given, 
they  should  be  brief  and  accurate.  It  is  also  a  mistake  to  try 
to  use  the  language  of  the  book  or  the  instructor.  Such  artificial 
work  stifles  thought  and  conceals  the  condition  of  the  learner. 

The  subject  of  analysis  should  not  be  unduly  emphasized.  A  correct 
solution  may  generally  be  accepted  as  evidence  that  the  correct  analysis 
has  been  made. 


COMMON  FRACTIONS  129 

ORAL  EXERCISE 

In.  the  following  problems  first  find  each  result  as  required,  and  then 
give  a  brief,  accurate  explanation  of  the  steps  taken  in  the  solution.  Do 
not  use  pen  or  pencil. 

1.  If  2  T.  cost  88,  what  will  5  T.  cost? 

Suggestion.  $20;  since  2  T.  cost  $8,  5  T.,  which  are  2|  times  2  T.,  will 
cost  2  i  times  $8,  or  $20. 

2.  24  is  1^  of  what  number  ?  f  of  what  number  ?  -f^  of  what 
number  ? 

3.  220  is  ^  less  than  what  number?  450  is  J  less  than 
what  number  ? 

4.  A,  having  spent  ^  of  his  money,  finds  he  has  884  left. 
How  much  had  he  at  first  ? 

5.  1124  is  i  more  than  what  sum  of  money?  fSOO  is  J 
more  than  what  sum  of  money? 

6.  A  man  sold  -f^  of  an  acre  of  land  for  $35.  At  that  rate 
what  is  his  entire  farm  of  100  acres  worth  ? 

7.  A  man  bought  a  stock  of  goods  and  sold  it  at  J 
above  cost.  If  he  received  8275,  what  was  the  cost  of  the 
goods  ? 

8.  B  bought  a  stock  of  goods  which  he  sold  at  ^  below  cost. 
If  he  received  for  the  sale  of  the  goods  8240,  what  was  the  cost 
and  what  was  his  loss  ? 

9.  -^Q  of  the  students  in  a  high  school  are  girls  and  the  re- 
mainder are  boys.  If  the  number  of  boys  is  350,  how  many 
scholars  in  the  school  ? 

10.  A  bought  a  quantity  of  wheat  which  he  sold  at  J  above 
cost.  If  he  received  8  300  for  the  wheat,  what  did  it  cost  him 
and  what  was  his  gain  ? 

11.  A  bought  a  quantity  of  dry  goods  and  sold  them  so  as  to 
realize  ^  more  than  the  cost.  If  the  selling  price  was  8720, 
what  was  the  cost  and  what  was  the  gain  ? 

12.  D  bought  a  stock  of  carpeting  which  he  was  obliged  to 
sell  at  J  below  cost.  If  he  received  8750  for  the  sale  of  the  car- 
peting, what  was  the  cost  of  same,  and  what  was  his  loss  ? 


130  CONCISE   BUSINESS   ARITHMETIC 

WRITTEN  EXERCISE 
In  the  following  problems  give  both  analysis  and  computation. 

1.  If  I  lb.  of  tea  cost  21^,  what  will  9^  lb.  cost  ? 

Computation  Analysis 

9|  =  J^  9|  =  V- ;  91  is  therefore  19  times  i     If  |  lb.  cost 

19  X  21  j?  =  $  3.99       2i  f,  9i  lb.  will  cost  19  times  21  f,  or  |3.99. 

2.  If  I  of  a  pound  of  tea  cost  42  ^,  what  will  35|  lb.  cost  ? 

3.  If  a  drain  can  be  dug  in  IT  da.  by  45  men,  how  many 
men  will  it  take  to  dig  ^  of  it  in  3  da.? 

4.  In  what  time  will  3  boys  at  f  0.621-  per  day  earn  as  much 
as  4  men  at  $2.25  each  per  day  will  earn  in  45|  da.? 

5.  A  spends  872  per  week  or  |  of  his  income  ;  B  saves 
848  per  week  or  |  of  his  income.  How  long  will  it  take  A 
to  save  as  much  as  B  saves  in  five  weeks? 

6.  If  115  bu.  of  wheat  are  required  to  make  23  bbl.  of 
flour,  how  many  bushels  will  he  required  to  make  50  bbl.  of 
flour  ?  117  bbl.  of  flour  ?  259  bbl.  of  flour  ? 

ORAL  REVIEW  EXERCISE 

1.  .05x6x0x21  =  ? 

2.  $0.75  is  what  part  of  $3? 

3.  What  is  the  sum  of  ^,  |,  ^,  and  -^  ? 

4.  Find  the  value  of  .45 +  (.25  x  5) -.04. 

5.  60  is  f  of  what  number?  |?  f  ?  -f?  f  ? 

6.  At  25^  a  yard,  what  will  2|^  yd.  of  cloth  cost? 

7.  y  is  1^  of  what  number?     |  is  |  of  what  number? 

8.  If  I  of  an  acre  of  land  costs  $75,  what  will  50  A.  cost  ? 

9.  If  I  of  a  number  is  84,  what  is  5  times  the  same  number  ? 

10.  The  dividend  is  4^  and   the   quotient  is   6|;  what    is 
the  divisor? 

11.  If  6  bu.  of  apples  cost  $15,  what  will   80   bu.  cost  at 
the  same  rate  ? 

12.  At   $460    per   half   mile,  what    will    be    the    cost    of 
grading  6  mi.  of  road? 


COMMON  FRACTIONS  131 

13.  How  much  will  4  carpenters  earn  in  10  da.  at  the 
rate  of  $2.25  each  per  day? 

14.  At  $4.50  per  cord,  what  will  be  the  cost  of  4 J  cd. 
of  wood  ?  of  61  cd.  ?  of  121  cd.  ?  of  71  cd.  ? 

15.  A  bought  a  horse  for  $96  and  sold  it  for  |-  of  its 
cost.     What  part  of  the  cost  was  the  loss  sustained  ? 

16.  A  bought  4 J  yd.  of  velvet  at  $5.20  per  yard  and 
gave  in  payment  a  $50  bill.  How  much  change  should  he 
receive  ? 

17.  I  sold  5  A.  of  land  for  $375  and  sustained  a  loss  equal 
to  ^  of  the  original  cost  of  the  land.  What  did  the  land  cost 
per  acre  ? 

18.  D  and  E  agree  to  mow  a  field  for  $36.  If  D  can  do 
as  much  in  2  da.  as  E  can  do  in  3,  how  should  the  money 
be  divided? 

19.  N  sold  a  watch  to  O  and  received  J  more  than  it 
cost  him.  If  O  paid  $64  for  the  watch,  what  did  it  cost  N? 
What  per  cent  did  N  gain  ? 

20.  A  earns  $125  per  month.  Of  this  sum  he  spends  $75 
and  saves  the  remainder.  What  part  of  his  monthly  earn- 
ings does  he  save  ?     What  per  cent  ? 

WRITTEN  REVIEW  EXERCISE 

1.  Find  the  cost  of  1100  eggs  at  23|^  per  dozen. 

2.  Counting  2000  lb.  to  a  ton,  find  the  cost  of  5|  T.  of 
steel  at  1^^^  per  pound. 

3.  When  flour  is  sold  at  $6.02  per  barrel  of  196  lb.,  what 
should  be  paid  for  5b^  lb.  ? 

4.  I  bought  300  bbl.  of  flour  at  $5.75  per  barrel.  At  what 
price  must  I  sell  it  per  barrel  in  order  to  gain  $150  ? 

5.  The  cost  of  200  bu.  of  wheat  was  $204.50  and  the 
selling  price  $212.35.     What  was  the  gain  per  bushel? 

6.  A  can  do  a  piece  of  work  in  5^  da.  and  B  in  1^  da. 
If  they  join  in  the  completion  of  the  work,  how  long  will  it 
take  them? 


132  CO:^^CISE   BUSINESS   ARITHMETIC 

7.  How  much  will  7  men  earn  in  6  da.,  working  10  hr.  per 
day,  at  25  ^  per  Lour? 

8.  At  $2.50  per  day  of  8  hr.,  how  much  should  a  man 
receive  for  11 J  hours'  work  ? 

9.  A  boy  works  4 J  da.  at  the  rate  of  $5.75  per  week  of  6 
da.     How  much  does  he  earn  ? 

10.  W,  in  1  of  a  day,  earns  $1.25,  and  Y,  in  i  of  a  day,  earns 
$0.87|.     How  much  will  the  two  together  earn  in  40 J  da.  ? 

11.  A  and  B  together  can  do  a  piece  of  work  in  10  da. 
If  A  can  complete  the  work  alone  in  16  da.,  how  long  will 
it  take  B  to  do  it? 

12.  Nov.  1,  in  a  recent  year,  was  on  Tuesday.  How  much  did 
B  earn  during  November  if  he  was  employed  every  working  day 
at  the  rate  of  $3.75  per  day? 

13.  In  one  year  the  cotton  produced  in  the  United  States 
approximated  14,000,000  bales  of  500  lb.  each.  If  Texas 
produced  ^  of  the  crop,  Georgia  i.  South  Carolina  i,  and  Ala- 
bama 1,  what  was  the  value  of  the  cotton  produced  in  each 
state,  at  101/  per  pound  ? 

14.  In  one  year  the  value  of  the  cotton  crop  (including  the 
seed)  in  Texas  was  1188,000,000.  The  value  of  the  cotton  seed 
was  125,000,000.  The  value  of  the  cotton  was  what  fraction 
of  the  total  value  ?  The  value  of  the  seed  was  what  fraction 
of  the  total  value  ?     (Express  decimally,  using  three  places.) 

15.  In  one  day  14,310  beef  cattle  were  received  at  the  Union 
Stock  Yards,  in  Chicago.  If  |-  of  the  number  were  of  an  average 
weight  of  1056  lb.  and  sold  for  $6.80  per  hundred  pounds,  and  if 
the  remainder  were  of  an  average  weight  of  1192  lb.  and  sold  at 
$6.95  per  hundred  pounds,  what  was  the  total  value  of  the  cattle  ? 

16.  In  one  year  the  approximate  production  of  sugar  in  the 
United  States  (including  Hawaii  and  Porto  Rico)  was  as  follows : 
beet  sugar,  1,240,000,000  lb.;  cane  sugar,  1,108,000  short  tons. 
If  the  beet  sugar  was  worth  I^^q/  per  pound,  and  the  cane 
sugar  ly^Q-/  per  pound,  what  was  the  total  value  of  the  crop? 
(The  price  is  based  on  the  export  value  of  refined  sugar.) 


COMMOK   i^EACTIONS 


133 


GKAPHIC   OUTLINE 

A  comparison  of  the  money  value  of  the  wheat  crop,  and  the  fire  losses 
paid  bj  insurance  companies,  in  the  United  States,  1890  to  1899  inclusive. 
,-  -value  of  wheat  crop.    value  of  fire  losses. 


1890 

1891 

1892 

1893 

1894 

1895 

1896 

1897 

1898 

1899 

800  million  dollars 

700  million  dollars 

GOO  million  dollars 

500  million  dollars 

A 

400  million  dollars 

/\ 

t\ 

300  milUon  dollars 

i 

\ 
\ 
\ 

\ 

. / 

1              X 

\ 

•"" 

200  million  dollars 

\ 

___„ 

./' 

100  million  dollars 

1 

, . 

WRITTEN    EXERCISE 

1.  The  figures  below  give  the  value  of  the  wheat  crop,  and  the 
fire  losses  paid  by  fire  msurance  companies,  in  the  United  States, 
for  the  years  1890  to  1899  inclusive.   (See  Graphic  Outline.) 

Farm  Val.  of  Wheat  Fire  Losses 

1890  $334,773,678  $108,993,792 

1891  513,473,711  143,764,967 

1892  322,111,881  151,516,098 

1893  213,171,381  167,544,370 

1894  225,902,025  140,006,484 

1895  237,938,998  142,110,233 

1896  310,602,593  118,737,420 

1897  428,547,121  116,254,575 

1898  392,770,320  130,593,505 

1899  319,545,259  153,597,830 


134  CONCISE   BUSINESS   ARITHMETIC 

2.  Make  a  graphic  outline  comparing  the  wheat  crop,  and  the 
fire  losses  paid  by  the  fire  insurance  companies,  in  the  United 
States,  for  the  years  1880  to  1889  inclusive. 


Farm  Val.  of  Wheat 

Fire  Losses 

1880 

$474,201,850 

$74,643,400 

1881 

456,880,427 

81,280,900 

1882  - 

445,602,123 

84,505,024 

1883 

883,649,272 

100,149,228 

1884 

830,862,260 

110,008,611 

1885 

275,320,390 

102,813,796 

1886 

314,226,020 

104,924,750 

1887 

810,612,960 

120,283,055 

1888 

385,248,030 

110,885,665 

1889 

342,491,707 

123,046,833 

3.  Make  a  graphic  outline  comparing  the  wheat  crop,  the  cotton 
crop,  and  the  fire  losses  paid  by*  the  fire  insurance  companies,  in 
the  United  States,  for  the  years  1900  to  1909  inclusive. 


Farm  Yal.  of  Wheat 

Farm  Val.  of  Cotton 

Fire  Losses 

1900 

$323,515,177 

$515,828,431 

$160,929,805 

1901 

467,350,156 

439,166,710 

165,817,810 

1902 

422,224,117 

501,897,135 

161,087,040 

1903 

443,024,826 

660,549,230 

145,302,155 

1904 

510,489,874 

652,031,626 

229,198,050 

1905 

518,372,727 

632,298,332 

165,221,650 

1906 

490,332,760 

721,647,237 

518,611,800 

1907 

554,437,000 

700,956,011 

215,084,709 

1908 

616,826,000 

681,230,956 

217,885,850 

1909 

730,046,000 

812,089,833 

188,705,150 

Use  a  dotted  line  to  represent  the  cotton  crop. 

The  figures  representing  the  fire  losses  do  not  include  the  cost  of  main- 
taining fire  departments,  nor  the  losses  sustained  by  the  interruption  of 
business. 

The  United  States  exceeds  all  other  countries  in  losses  by  fire.  A  large 
per  cent  of  these  losses  are  due  to  carelessness. 


commo:n^  feactions  135 

ORAL   REVIEW   EXERCISE 

1.  f  of  36  is  what  part  of  81  ? 

2.  Multiply  126  by  101;  92  by  102. 

3.  Divide  41  by  2| ;  3|  by  21. 

4.  Find  the  cost  of  each  of  the  following : 

a,    35  bu.  of  seed  at  35/  per  busheL 
h,    65  A.  of  land  at  S65  per  acre. 
c,    45  yd.  of  cloth  at  45/  per  yard 

5.  Divide  I  by  A;  |byf;  f  by  |. 

6.  Multiply  36  by  I ;  49  by  f ;  55  by  J^. 

7.  What  is  the  square  of  15  ?  of  1.5  ?  of  11  ? 

8.  64x|  =  ?  64^^  =  ?  i  +  i  +  J=? 

9.  How  many  yards  of  cloth  can  be  bought  for  $25  at  121/ 
per  yard  ? 

10.  If  it  costs  $7.50  to  harvest  61  A.  of  com,  what  will  it 
cost  to  harvest  65  A.  ? 

11.  An  agent  received  $7.20  for  collecting  a  debt,  and  the 
merchant  received  $232.80.     What  was  the  total  debt? 

12.  C  and  D  received  $  21.75  for  work  done  jointly.  If  C  does 
only  half  as  much  work  as  D,  how  should  the  money  be  divided  ? 

13.  If  a  lot  of  articles  were  bought  at  the  rate  of  3  for  2/  and 
sold  at  the  rate  of  2  for  3  /,  how  many  must  be  sold  to  gain  $  5  ? 

14.  A  and  B  received  $34  for  work  done  jointly.  If  A  can 
do  as  much  work  in  8  da.  as  B  can  do  in  9  da.,  how  should  the 
money  be  divided  ? 

15.  Name  the  results  quickly : 

a.  A  can  do  a  piece  of  work  in  4  da.,  and  B  in  5  da.  If  they 
work  together,  in  how  many  days  will  they  finish  the  task  ? 

h.  F  can  do  a  piece  of  work  in  31  da.,  and  G  in  5  da.  If  they 
work  together,  in  how  many  days  will  they  finish  the  task  ? 

c,  C  can  do  a  piece  of  work  in  2  da.,  D  in  3  da.,  and  E  in  4  da. 
If  they  work  together,  in  how  many  days  will  they  finish  the  task  ? 

d.  H  and  J  together  can  do  a  piece  of  work  in  20  da.  If  H 
alone  can  do  the  work  in  30  da.,  in  how  many  days  can  J  alone 
do  the  work  ? 


136  CONCISE   BUSINESS   ARITHMETIC 

written  exercise 
Problems  of  the  Farm 

1.  If  15  sheep  consume  5785  lb.  of  dry  fodder  in  a  year,  what 
is  the  cost  per  sheep  if  the  fodder  is  worth  S8.50  per  ton  ? 

2.  If  eggs  are  worth  24/  per  dozen,  what  is  the  difference 
in  the  value  of  two  hens,  in  a  year,  if  one  lays  180  eggs  and  the 
other  lays  96  eggs  ? 

3.  An  apple  tree  produced  9i  bu.  of  apples,  61-  bu.  of  which 
graded  as  "  firsts  "  and  the  remainder  as  "  seconds."  What  frac- 
tional part  of  the  yield  were  firsts,  and  what  fractional  part  were 
seconds  ? 

4.  The  apple  tree  referred  to  in  Ex.  3  was  sprayed  the  year 
following,  and  that  year  it  produced  10  i  bu.  of  which  9^  bu. 
were  firsts  and  the  remainder  seconds.  What  fractional  part  of 
the  yield  were  firsts  ?    What  part  were  seconds  ? 

5.  If  the  apples  referred  to  in  Exs.  3  and  4  were  sold  at  S1.20 
per  bushel  for  firsts  and  70/  a  bushel  for  seconds,  what  was  the 
value  of  the  spraying  ? 

6.  It  is  estimated  that  a  quail  in  one  year  eats  28/  worth 
of  grain  and  saves  $1.68  worth  of  grain  by  destroying  insects 
and  weeds.  What  is  the  value  of  a  pair  of  quails  to  the  farmer 
annually,  not  counting  the  value  of  the  brood  ? 

7.  An  undrained  field  produced  24  bu.  of  grain  per  acre,  and 
after  being  drained  it  produced  33  bu.  per  acre.  What  was  the 
fractional  increase  ?  What  was  the  value  of  the  increase  if  the 
grain  sold  for  55i-/  per  bushel  ? 

8.  A  flock  of  hens  averaged  78  eggs  each  per  year.  What 
would  be  the  value  to  the  farmer  of  introducing  a  better  breed 
of  hens  that  would  produce  120  eggs  each  per  year,  if  he  kept 
a  flock  of  40  hens,  and  received  24/  per  dozen  for  the  eggs  ? 

9.  If  6  A.  of  unfertilized  land  produced  275  bu.  of  corn,  and 
if  fertilized,  it  would  have  produced  350  bu.,  what  would  the 
farmer  have  gained  by  fertilizing  the  land  if  the  corn  was  sold 
for  68/  per  bushel,  and  the  fertilizer  cost  S  24  per  ton,  and  400  lb. 
were  used  on  each  acre  ? 


COMMON   FRACTIONS  l37 

WRITTEN  REVIEW  TEST 
(Time,  approximately,  forty  minutes) 

1.  A,  B,  and  C  hire  a  pasture  for  $  81.  A  puts  in  6  cows  for 
4  mo. ;  B,  6  cows  for  6  mo. ;  and  C,  6  cows  for  5  mo.  "What  sum 
should  each  pay  ? 

2.  A  man  owned  |-  of  a  tract  of  land ;  he  sold  |-  of  his  share 
for  $14,504.46.  At  that  rate,  what  was  the  value  of  his  original 
share  ?    What  was  the  whole  tract  worth  ? 

3.  The  owner  of  a  house  received  a  net  yearly  income  from 
rental  of  S408.90,  after  paying  the  following  :  insurance,  $64.20  ; 
taxes,  $74.50  ;  repairs,  $28.40.    What  was  the  monthly  rental? 

4.  A  man  drew  i  of  his  money  from  the  bank  and  then  paid 
bills  of  the  following  amounts:  $12.50,  $18.25,  and  $7.50;  he 
then  had  left  in  cash  $11.75.  What  sum  had  he  in  the  bank 
before  drawing  the  check  ? 

5.  A  man  placed  a  mortgage  on  his  house  and  lot  for  $2967. 
The  lot  cost  $2720 ;  the  improvements,  $260.50;  and  the  dwell- 
ing, $5920.50.  The  mortgage  was  what  fractional  part  of  the 
total  value  of  the  property  ? 

6.  At  the  end  of  a  season  a  dealer  sold  a  machine  for  $64, 
after  reducing  the  marked  price  ^.  If  he  still  gained  ^-  of  the 
cost,  what  was  the  first  cost?  The  marked  price  was  what 
fraction  above  the  cost  price  ? 

7.  From  dictation,  write  results  for  the  following:  -^  of 
25J;  J  of  26J;  i  of  361  ;  i  of  I71  ;  1  of  42|;  |  of  28J;  ^\  of 
221 .  1  of  641 ;  1  of  50 1;  J^  of  35t ;  J^  of  501. 

8.  A  merchant  closed  his  business  under  the  following  con- 
ditions: resources,  $22,455.20;  liabihties,  $33,682.80.  What 
fractional  part  of  his  debts  can  he  pay  ?  If  he  owes  James  S. 
Brown  $202.50,  how  much  will  Brown  receive  in  settlement? 

9.  A,  B,  and  C  are  partners  in  a  mercantile  business  in 
which  A  has  invested  $9180  ;  B,  $6120  ;  and  C,  $3060.  At  the 
end  of  1  yr.  they  divided  a  gain  of  $3060.90.  If  each  partner 
received  of  the  gain  according  to  his  fractional  part  of  the 
investment,  how  much  did  each  receive  ? 


CHAPTER  X 

ALIQUOT  PARTS 

171.   An    aliquot  part  of   a  number  is   a  part  that  is  con- 
tained in  the  number  an  integral  number  of  times. 

Thus,  2^,  3^,  and  5  are  aliquot  parts  of  10. 
ORAL  EXERCISE 

1.  How  many  cents  in  $l?  in  |J?  in  S^?  in  |1? 

2.  What  aliquot  part  of  $1  is  25^?  50^?  6|^?  121^? 

3.  Read  aloud  the  following,  supplying  the  missing  terms : 
16x50)2^  =  16x|i^iof$16r  16x25y  =  16x$i  =  ^ofil6; 

16xl2l^=16x$ = of  116;  16x61^=16x8 

= of  $16. 

4.  Give  a  short  method  for  finding  the  cost  when  the  quan- 
tity is  given  and  the  price  is  50^;  25^;  12^^ ;  6^^. 

5.  What  is  the  cost  of  160  yd.  of  dress  goods  at  $1?  at  50^? 
at  25^?  at  121^?  at  6^^? 

6.  How  many  cents  in  $1?  in  $1?  in  $^-^?  in  $^^5?  in  $|? 
in$^?  in$Jo? 

7.  What  aliquot  part  of  $1  is  331^?    16f^?    8^^?    62^? 
14f^?  20^?  10^? 

8.  Read  aloud  the  following,  supplying  the  missing  terms : 

140xl4f^  =  140  X  i|  =  |  of  $140;  90  x  6|^  =  90  x  $ 

= of  890;  90x20^  =  90x8 = of  890. 

9.  Read  aloud  the  following,  supplying  tlie  missing  terms : 

240  X  33iy  =  240  X  8 =  |    of    8240 ;    240  x  16f  =  240  x 

8J  = of  8240;  240x12^^  =  240x8 = of  8  240. 

10.  Give  a  short  method  for  finding  the  cost  when  the  quan- 
tity is  given  and  the  price  is  33  J  ^ ;    16|^;  81^;  6f^;  14f^. 

11.  Find  the  cost  of  960  yd.  of  cloth  at  33J^;  at  16|^;  at  Sy. 

138 


ALIQUOT  PARTS  139 

ORAL  EXERCISE 

State  the  cost  of: 

1.  240  1b.  tea  at  50/;  at  331^;  at  25^. 

2.  3601b.  coffee  at  331^;  at  25^;  at  20^;  at  12J^. 

3.  720  gal.  cider  at  6^^;  at  6|^;  at  10^;  at  12|-^. 

4.  2400  doz.  eggs  at  12^^;  at  16|^;  at  20^;  at  25^. 

5.  2400  yd.  prints  at  SJ^;  at  6|^  ;  at  6|^;  at  121^. 

6.  960  yd.  cotton  at  61^;  at  81^;  at6fj^;  at  10^;  at  121^. 

7.  2040  yd.  plaids  at  50^;  at  331^;  at25j^;  at  20^;  at  16f  ^. 

8.  480  1b.  lard  at  81^;  at6J^;  at  121)^;   at  16|^;  at  10^. 

9.  3600  lb.  raisins  at  12|-^;  atl6|^;  at  20^;  at  25^;  at  33^^. 

10.  480  yd.  lining  at  81^;  at6|^;  at  10^;  at  121^;  at6|^. 

11.  4200  yd.  Silesia  at  W;  at  20)^ ;  at  12^^:  at  16f  ^ ;  at  14f  ^. 

12.  1500  yd.  plaids  at  $1;  at  50^;  at  33ij^;  at  25^;  at  20^. 

13.  420  yd.  stripe  at  10^;  atl2i^;  at  14|y ;  at  16f  ^;  at  25ji^. 

14.  120  yd.  gingham  at  8i^;  at6|/;  at6|^;  at  loV;  at  121^. 

15.  1240  yd.  wash  silk  at  25^;  at  50^;  at  331  ^;  at  20^. 

16.  At  the  rate  of  3  for  50^,  what   will  27  handkerchiefs 
cost? 

17.  At  33i^  per  half  dozen,  what  will  12  doz.  handkerchiefs 
cost?  17  doz.?  25  doz.?  7 J  doz.?  4|  doz.? 

18.  A  merchant  bought  cloth  at  33 J  ^  per  yard  and  sold  it 
at  50^  per  yard.     What  was  his  gain  on  1680  yd.? 

ORAL  EXERCISE 

1.  What  is  the  cost  of  121  yd.  of  silk  at  96  ^  per  yard? 
Suggestion.    The  cost  of  12|  yd.  at  9Qj^  =  the  cost  of  96  yd.  at  12^^. 

Interchanging  the  multiplicand  and  multiplier  considered  as  abstract  numbers 
does  not  affect  the  product. 

2.  Find  the  cost  of  25  yd.  of  silk  at  11.72  per  yard. 
Suggestion.    The  cost  of  25  yd.  at$  1.72  (172^)  =  the  cost  of  172  yd.  at  2bf, 

3.  Find  the  cost  of : 

a,  25  yd.  at  16^.       e.    6J  lb.  at  32^.       e.    25  yd.  at  84^. 

b,  12|^  yd.  at  48^.     d.    12Jlb.at80^.     /.    121  yd.  at  11.75. 


140 


COKCISE  BUSIKESS   AEITHMETIC 

Table  of  Aliquot  Parts 


Nos. 

I's 

i's 

Fs 

tVs 

fs 

•rs 

tV's 

I'^'S 

i's 

Iter's 

1 

.50 

.25 

.121 

.061 

.331 

.161 

.081 

.061 

.20 

.10 

10 

5. 

n 

H 

.62^ 

H 

If 

.83^ 

.66f 

2. 

1. 

100 

50. 

25. 

m 

n 

33^ 

16f 

8^ 

6f 

20. 

10. 

1000 

500. 

250. 

125. 

62^ 

333^ 

166|- 

83^ 

66f 

200. 

100. 

WRITTEN  EXERCISE 

In  the  three  problems  following  make  all  the  extensions  mentally/. 

1.  Without  copying,  find  quickly  the  total  cost  of : 
84  lb.  tea  at  50^.  6J  lb.  tea  at  64^. 

75  lb.  tea  at  331^.  25  lb.  cocoa  at  52^. 

72  lb.  cofPee  at  25^.  121  lb.  cocoa  at  48^. 

84  lb.  coffee  at  331^.  .               860  lb.  codfish  at  6|^. 

25  lb.  coffee  at  28  j2^.  66  lb.  crackers  at  8^^. 

88  lb.  candy  at  121  jz^.  25  lb.  chocolate  at  36^. 

24  lb.  tapioca  at  6J^.  25  cs.  horseradish  at  64^. 

2.  Without  copying,  find  quickly  the  total  cost  of  : 

25  yd.  silk  at  84^. 
12|  yd.  silk  at  dQfl. 
750  pc.  lace  at  6f  ^. 
112  yd.  ticking  at  6Jj^. 
210  yd.  plaids  at  33^^. 
128  gro.  buttons  at  12^^. 
68  yd.  lansdowne  at  50^. 


77  yd.  duck  at  14f  ^. 

6|  gro.  buttons  at  32^. 

155  yd.  cheviot  at  20)^. 

96  yd.  gingham  at  8^^. 

84  yd.  shirting  at  121  ^. 

25  doz.  spools  thread  at  25^. 

168  yd.  striped  denim  at  S^  ^. 


3.    Without  copying,  find  quickly  the  total  cost  of 


25  bu.  corn  at  64^. 
25  bu.  corn  at  $0.72. 
121  bu.  oats  at  $0.36. 
25  bu.  beans  at  $2.80. 
121  bu.  wheat  at  $1.04. 
12Jbu.  millet  at  $1.24. 
25  bu.  clover  seed  at  $3.60. 
50  bu.  clover  seed  at  $3.75. 


25  bu.  corn  at  $0.84. 
25  bu.  corn  at  $0.44. 
25  bu.  oats  ^t  $0.35. 
12Jbu.  rye  at  $1.04. 
6Jbu.  wheat  at  $1.20. 
6Jbu.  wheat  at  $1.12. 
25  bu.  timothy  seed  at  $2.40. 
50  bu.  timothy  seed  at  $2.75. 


ALIQUOT  PAETS  141 

ORAL  EXERCISE 

1.  Multiply  by  10:  4;  15;  .07  ;  8^;  $1.12;  124.60;  $12,125. 

2.  Multiply  by   100:    3;   17;     .09;    12^;    $1.64;    $21.17. 

3.  Multiply  by  1000:  7;    29;    .19;    15^;  $1.75;    $23.72. 

4.  What  aliquot  part  of  $10  is  $2.50  ?     Find  the  cost  of  16 
articles  at  $10  each;  at  $2.50  each. 

5.  Find  the  cost  of  84  bu.  of  wheat  at  $1.25. 

Solution.    $1.25  is  I  of  $10.  84bu.  at  $10  =  $840;  ^  of  $840  =  $106. 

6.  Formulate  a  short  method  for  finding  the  cost  when  the 
quantity  is  given  and  the  price  is  $1.25. 

Solution.   $1.25  is  |  of  $10;  hence,  multiply  the  quantity  by  10  and  take  \ 
of  the  product. 

7.  Formulate  a  short  method  for  finding  the  cost  when  the 
quantity  is  given  and  the  price  is  $2.50 ;  $3.33^;    $1.66|. 

8.  Find  the  cost  of  168  yd.  of  cloth  at  $1.25;  at  $2.50; 
at  $3,331;  at  $1.66|. 

9.  What  aliquot  part  of  $100  is  $25  ?    $12.50?  $6.25  ? 

10.  Find  the  cost  of  72  chairs  at  $  25  each. 

Solution.    72   chairs   at  $100  =  $7200;  but  the  price  is  $25,  "which  is  \  of 
$100;  therefore,  \  of  $7200,  or  $1800,  is  the  required  cost. 

11.  Give  a  short  method  for  multiplying  any  number  by  25 ; 
by  121;  by6i;  by  331;  by  81. 

12.  Find  the  cost  of  25  T.  coal  at  $7.20 ;  of  6^  T. ;  of  121  T. 

13.  What  aliquot  part  of  1000  is  250?    500?    125?    621? 
3331?   166|?    200?    100?    831?    66|? 

14.  Formulate  a  short  method  for   multiplying  a    number 
by  250. 

Solution.  Since  250  =  ■^°^°-^,  multiply  by  1000  and  take  \  of  the  product. 

15.  Give  a  short  method  for  finding  the  cost  when  the  quan- 
tity is  given  and  the  price  is  $125 ;  $166|. 

16.  Multiply  84  by  50;  by  25;  by  121;  by  16f ;  by  331 

17.  Multiply  160  by  21;  by  IJ ;  by  121;  by  125;  by  621 

18.  Multiply  240  by  31;  by  1|;  by  331;  by  16f ;  by  338f 


142  CONCISE   BUSINESS   ARITHMETIC 

•    19.    Find  the  cost  of  250  sofa  beds  at  $32  each. 

Solution.  The  cost  of  250  beds  at  $32  =  the  cost  of  32  beds  at  $250.  The 
cost  of  32  beds  at  $1000  =  $32,000  ;  but  the  price  is  $250,  which  is  {  of  $1000 ; 
therefore,  I  of  $32,000,  or  $8000,  is  the  required  cost. 

20.  Find  the  cost  of  720  couches  at  $12.50  each. 

21.  Find  the  cost  of  440  lb.  sugar  at  21^. 

Solution.  2^^  is  I  of  10^.  The  cost  of  440  lb.  at  10^  =  $44 ;  but  the  price  is 
2Jj^,  therefore,  |  of  $44,  or  $11  =  the  required  cost. 

22.  Formulate  a  short  method  for  finding  the  cost  when  the 

quantity  is  given  and  the  price  is  1 1  ,^. 

Solution.  1^^  =  |  of  10^ ;  hence,  point  off  one  place  in  the  quantity  and  take 
I  of  the  result. 

23.  Give  a  short  method  for  finding  the  cost  when  the  quan- 
tity is  given  and  the  price  is  2^^;  S^f^ ;  IJ^. 

24.  Find  the  cost  of  160  lb.  at  2^;  at  l^^;  at  2^; 
at  1|^.     Also  of  240  lb.  at  each  of  these  prices. 

25.  Find  the  cost  of  2400  lb.  at  2i  ^;  at  1^^;  at  3^^; 
at  1|^.     Also  of  360  lb.  at  each  of  these  prices. 

ORAL   EXERCISE 
Bt/  inspection  find  the  cost  of : 

1.  25  lb.  tea  at  54^.  16.  1\  yd.  silk  at  88f^. 

2.  25  lb.  tea  at  331^.  17.  64  pc.  lace  at  $1.25. 

3.  125  lb.  tea  at  64^.  is.  125  yd.  silk  at  11.12. 

4.  6^  A.  land  at  $112.  19.  1250  bbl.  beef  at  $24. 

5.  25  T.  coal  at  $8.40.  20.  78  yd.  velvet  at  $2.50. 

6.  25  T.  coal  at  $5.20.  21.  2^  bu.  potatoes  at  96^. 

7.  18  T.  coal  at  $6.25.  22.  640  bu.  apples  at  871^. 

8.  164  A.  land  at  $25.  23.  840  yd.  prints  at  16f  ^. 

9.  72  T.  coal  at  $6.25.  24,  121  bu.  potatoes  at  64^. 

10.  250  yd.  silk  at  88  ^.  25.   84  bookcases  at  $12.50. 

11.  250  yd.  silk  at  96^.  26.  810  bbl.  pork  at  $12.50. 

12.  25  pc.  lace  at  $6.60.  27.  125  yd.  crepon  at  $3.60. 

13.  250  yd.  silk  at  $1.12.  28.  12^  yd.  cheviot  at  $1.04. 

14.  192  A.  land  at  $12.50.  29.  24  oak  sideboards  at  $125. 

15.  165  gro.  buttons  at  33^^.  30.  12^  yd.  gunner's  duck  at  48  A 


ALIQUOT  PARTS  .143 

WRITTEN   EXERCISE 

In  the  following  problems  make  all  the  extensions  mentally.    See 
how  many  of  the  problems  can  be  done  in  10  minutes. 

1.  Without  copying,  find  the  total  cost  of  : 

425  lb.  at  10  /.            2500  lb.  at  64 1  24  lb.  at  11  ^. 

310  lb.  at  20  ^.            1600  lb.  at  25  ^.  48  lb.  at  2i  ^. 

100  lb.  at  14  ^.            1893  lb.  at  31  ^.  21  lb.  at  96  ^. 

1000  lb.  at  27  ^.            2500  lb.  at  14  ^.  125  lb.  at  24^. 

1000  lb.  at  41  i.            1400  lb.  at  25  ^.  192  lb.  at  31  ^. 

1250  lb.  at  44  ^. '           1250  lb.  at  88  ^.  88  lb.  at  121  f, 

2.  Without  copying,  find  the  total  cost  of : 

88  yd.  at  1 1  /.            174   yd.  at  10  p.  24  yd.  at  12  ^. 

72  yd.  at  31  ^.            123   yd.  at  11  ^.  78  yd.  at  3J  ^. 

104  yd.  at  2i  ^.            127   yd.  at  11  ^.  165  yd.  at  20  ^. 

480  yd.  at  61  ^.       '     246   yd.  at  25/.  114  yd.  at  6f /. 

360  yd.  at  81  ^.            1712  y^j.  at  10  /.  1280  yd.  at  6^  /. 

121  yd.  at  11  /.            178^  yd.  at  10  /.  192  yd.  at  331/. 

3.  Copy  and  find  the  total  cost  of  : 

450  lb.  at  11  /.             249  lb.  at  25  /.  6J  lb.  at  88  /. 

820  lb.  at  11  /.             240  lb.  at  31  /.  92  lb.  at  21  /. 

1200  lb.  at  41  /.             200  lb.  at  3|  /.  121  lb.  at  24  /. 

1400  lb.  at  61  /.             450  lb.  at  6f  /.  18  lb.  at  41  /. 

7961  lb.  at  50  ^.             791  ib.  at  40  /.  125  lb.  at  18  /. 

1293  lb.  at  30  ^.             78i  lb.  at  50  /.  648  lb.  at  61  /. 

1480  lb.  at  40  /.             750  lb.  at  331  ^.  1900  lb.  at  4 1  /. 

4.  Copy  and  find  the  total  cost  of  : 

750  gal.  at  81  /.             99  gal.  at  30  /.  360  gal.  at  5  /. 

488  gal.  at  6|  /.             60  gal.  at  6|  /.  625  gal.  at  64  /. 

640  gal.  at  61  /.             50  gal.  at  76  /.  810  gal.  at  IJ  /. 

194  gal.  at  50  /.             25  gal.  at  74  /.  920  gal.  at  21  /. 

176  gal.  at  25  /.           121  gal.  at  88  /.  165  gal.  at  6|  /. 

280  gal.  at  121  ^.           79  gal.  at  331  ^.  240  gal.  at  621  ^. 

720  gal.  at  331  ^.           20  gal.  at  $1.79.  666  gal.  at  66|  /. 

366  gal.  at  16f  ^.           6J  gal.  at  $1.96.  1680  gal.  at  16|/. 


144  CONCISE   BUSINESS   ARITHMETIC 

ORAL  EXERCISE 

1.  How  much  less  than  il  is  75^?  what  fractional  part 
of  f  1  less? 

2.  Find  the  cost  of  144  pc.  of  lace  at  15  P  per  piece. 

Solution.     At  $  1  per  piece  the  cost  would  be  f  144  ;  but  the  cost  is  not  1 1 
but  J  less  than  $  1.     Deducting  J  of  $  144,  the  result  is  $  108,  the  required  cost. 

3.  Find  the  cost  of  124  bookcases  at  $7.50. 

Solution.     $  7.50  is  ^  less  than  $  10.     $  1240  less   J   of   itself  =  $  930,  the 
required  result. 

4.  Formulate  a  rule  for  multiplying  a  number  by  .75;  by 
7|;  by  75;  by  750. 

5.  How  much  more  than  $1  is  $1.12|?  What  fractional 
part  of  fl  more? 

6.  Find  the  cost  of  84  yd.  of  silk  at  |1.16|  per  yard. 

Solution.     At  $  1  per  yard,  the  cost  would  be  $84  ;  but  $1.16|  is  ^  more 
than  $1.     Adding  ^  of  $84  to' itself,  the  result  is  $98,  the  required  cost. 

7.  Formulate  a  short  method  for  finding  the  cost  when 
the  quantity  is  given  and  the  price  is  $1.12|;  $1.16|; 
$1.33i;  $11.25;  f  112.50. 

8.  How  much  less  than  $1  is  87|^^?  what  fractional 
part  of  f  1  less?  Formulate  a  "short  method  for  multiplying  a 
number  by  87-|-. 

9.  Formulate  a  short  method  for  multiplying  a  number 
by  .831;  by  1.25. 

10.    Compare  the  cost  of  87^  yd.  at  64^  with  the  cost  of 
64  yd.  at  87^^. 

ORAL  EXERCISE 

State  the  cost  of: 

1.  24  yd.  at  15^.  7.   87^  yd.  at  $2.88.  13.     270  yd.  at  111^. 

2.  75  yd.  at  24^.  a     25  yd.  at  4^.       14.     144  yd.  at  11^^. 

3.  192  yd.  at  871^.  9.  28yd.at75^.  15.  Iliyd.atl8^. 

4.  240  yd.  at  83^^.  lo.  27  yd.  at  75^.  16.  1125  yd.  at  64^. 

5.  871  yd.  at  $2.48.  u.  75  yd.  at  84^.  17.  1125  yd.  at  32 f^. 

6.  176  yd.  at  11.121  12.  75  yd.  at  16)z^.  18.  1125  yd.  at  48 )Z^. 


ALIQUOT  PARTS 


145 


WRITTEN  REVIEW  EXERCISE 

1.  Find  the  total  of  the  costs  called  for  in  problems  1-15  in 
the  oral  exercise  at  the  top  of  page  139. 

2.  Find  the  total  cost  of  the  items  in  the  oral  exercise  at  the 
bottom  of  page  142;  of  the  items  in  the  oral  exercise  at  the 
bottom  of  page  144. 

3.  Find  the  total  cost  of  : 
84  yd.  at  7^.  98  yd.  at  9^. 

1121  yd.  at  5^.  79  yd.  at  11^. 

112|-  yd.  at  6^.  17  yd.  at  16^. 

4.  Find  the  total  cost  of : 
71  yd.  at  22^.  85  yd.  at  30^. 
31  yd.  at  U^,  17  yd.  at  25^. 
82  yd.  at  88^.               121  yd.  at  39^. 
71  yd.  at  72^.               250  yd.  at  64^. 

5.  Find  the  total  cost  of  : 
192  lb.  at  31^.  167  lb.  at  12J^. 
3841b.  at  61^.  184  lb.  at  371^. 
3781b.  at  6|^.              2164  lb.  at  2i^. 
1491b.  at  61^.             1369  lb.  at  21^. 

6.  Copy  and  find  the  amount  of  the  following  bills,  less  3  %  : 

a, 

Kochester,  N.Y.,  Aug.  2,  19 

Mr.  C.  G.  Garlic 

North  Rose,  N.Y. 

To  Smith,  Perkins  &  Co.,  Dr. 

Terms  :  cash,  less  3  %. 


72yd.  at  75^. 
87 J  yd.  at  88^. 
320  yd.  at  11^. 

30  yd.  at  7^^. 
24  yd.  at  SJ^. 
56  yd.  at  83^^. 
124  yd.  at  11.121 

1151f  lb.  at  10^. 
17211  lb.  at  15^. 
29111  lb.  at  33 J  ^. 
2706  1b.  at  331^. 


330  lb.  Granulated  Sugar 

6|<? 

32   ' 

'   Butter 

22^ 

64   ' 

'  Cheese 

16|^ 

75   ' 

'   Young  Hyson  Tea 

24;^ 

155   ' 

'   Dried  Apples 

Sf 

300  ' 

<  Brown  Sugar 

^\f 

60   * 

'   Oolong  Tea 

h\f 

125  ' 

'   Rio  Coffee 

28^ 

250  ' 

'  Mocha  Coffee 

24  j^ 

146 


CONCISE   BUSINESS   ARITHMETIC 


Buffalo,  N.Y.,  Aug.  5, 19 
Mr.  George  A.  Collier 

Savannah,  N.Y. 

Bought  of  George  H.  Buell  &  Co. 

Terms:  cash,  less  ,^%. 


72  pr.  Boys'  Hose  12 1^ 

18  doz.  Linen  Handkerchiefs  2.50 

18    "      Lace  Handkerchiefs  3.33^ 

78  yd.  Silk  Velvet  3.33^ 

75  pc.  Black  Ribbon  28^ 

347  yd.  Pontiac  Seersucker  Q\^ 

186   "    Washington  Cambric  12^^ 


ORAL  EXERCISE 

1.  At  33^  ^  per  pound,  how  many  pounds  of  coffee  can  be 
bought  for  $12? 

Solution.  .33^  =  $  | ;  3  pounds  can  be  bought  for  $  1 ;  then,  12  x  3  lb. 
=  36  lb.,  the  required  result. 

2.  When  the  cost  is  given  and  the  price  is  25^,  how  may 
the  quantity  be  found? 

Solution.  When  the  price  is  25  ^,  the  quantity  is  4  times  the  cost ;  hence, 
multiply  the  cost  by  4' 

3.  Give  a  short  method  for  finding  the  quantity  when  the 
cost  is  given  and  the  price  is  20^  ;  33^^;  12^^;  6^^;  6f  ^; 
16|^. 

4.  Formulate  a  short  method  for  dividing  any  number  by 
125. 

Solution.  125  is  I  of  1000  ;  then  the  quotient  by  125  will  be  8  times  the 
quotient  by  1000.  Therefore,  divide  by  1000  and  multiply  the  result  by  8.  Or, 
i\t  —  T^'  Therefore,  multiply  by  8  and  move  the  decimal  point  three 
places  to  the  left. 

5.  Give  a  short  method  for  dividing  by  6J. 

Solution.  Q\  =  r^oi  100  ;  then  the  quotient  by  6^  will  be  16  times  the 
quotient  by  100.  Therefore,  move  the  decimal  point  two  places  to  the  left  and 
multiply  the  result  by  16.  Or,  |  =  ^^.  Therefore,  multiply  by  16  and  move  the 
decimal  point  two  places  to  the  left. 


ALIQUOT  PARTS 


147 


6.  Give  a  short  method  for  dividing  a  number  by  12J  ;  by 
16|;  by  83J  ;  by  6| ;  by  66f ;  by  333J;  by  166|. 

7.  Formulate  a  short  method  for  dividing  a  number  by  .75. 

Solution.  .75  increased  by  |  of  itself  =  1.  When  the  divisor  is  1  the  quo- 
tient is  the  same  as  the  dividend.  Hence,  to  divide  a  number  by  .75  increase 
the  number  by  |  of  itself. 

8.  At  75  ^  per  bushel,  how  many  bushels  of  wheat  can  be 
bought  for  1144?  for  $192?  for  $240?  for  |780?  for  $1260? 
for  $360?  for  $1350?  for  $810? 

9.  At  $7.50  per  dozen,  how  many  dozen  men's  gloves  can 
be  bought  for  $1440? 

Solution.  $7.50  +  ^  of  itself  =  -$10.  To  divide  by  10  is  to  point  off  one 
place  to  the  left.  $  1440  -f  i  of  itself  =  $1920  ;  $  1920  -r-  $  10  =  192,  the  number 
of  dozen. 

10.  State  a  short  method  for  dividing  a  number  by  7 J ;  by 
75;  by  750. 

ORAL    EXERCISE 

Find  the  quantity : 


Price  per 

Price  PER 

Cost 

Yard 

Cost 

Pound 

1.   $65 

331^ 

7.   $75 

6|^ 

2.   $250 

25^ 

8.    $12 

If^ 

3.    $120 

6^^ 

9.   $25 

m^ 

4.    $215 

^^ 

10.   $38 

-^¥ 

5.    $126 

12|^ 

11.   $125 

fl.25 

6.    $125 

20^ 

12.   $420 

ISi*' 

WRITTEN   EXERCISE 


Find  the  quantity : 


Price  per 

Price  per 

Cost 

Yard 

Cost 

Bushel 

1. 

$570.00 

75^ 

6. 

$1721.00 

33jy 

2. 

$612.00 

13^ 

7. 

$1842.50 

26^ 

3. 

$274.50 

H^ 

8. 

$1785.00 

Sl^fl 

4. 

$281.50 

12|^ 

9. 

$2142.00 

33|^ 

5. 

$864.50 

12|^ 

10. 

$2720.50 

16|^ 

148 


CONCISE   BUSINESS   AEITHMETIG 


REVIEW   EXERCISE 

This  exercise  may  be  used  in  a  number  of  different  ways,  some  of  which 
are  suggested  below. 

1.  One  student  may  make  the  oral  extension,  using  the  first  quantity, 
60  yd.,  by  each  price  in  column  1 ;  a  second  student  may  use  the  same 
quantity  and  make  the  extension  by  each  price  in  column  2,  and  so  on  for 
the  ten  lists. 

2.  Each  student  in  the  class  may  take  the  same  quantity  and  make  the 
extension  by  each  price  in  column  1,  and  foot  the  extensions.  Compare 
results.  Such  an  exercise  should  occupy  one  minute.  This  work  may  be 
continued  for  ten  or  fifteen  minutes  daily,  as  the  instructor  desires,  a  different 
quantity  being  used  for  each  minute. 


1 

s 

3 

4 

5 

6 

7 

8 

9 

10 

50/ 

25/ 

66f/ 

60/ 

25/ 

61/ 

50/ 

75/ 

$1.50 

$1.33J 

20/ 

62J/ 

6|/ 

87i/ 

20/ 

16f/ 

90/ 

8J/ 

$1.25 

$1.66§ 

12i/ 

33J/ 

75/ 

sn/ 

60/ 

30/ 

10/ 

371/ 

$1.12i 

$1.20 

161/ 

30/ 

8J/ 

6J/ 

121/ 

66f/ 

e2i/ 

80/ 

$1.10 

$1.16§ 

90/ 

10/ 

40/ 

80/ 

331/ 

6|/ 

40/ 

871/ 

$1.75 

$1.30 

1.  Find  the  cost  of 


a.  60  jd. 
80  yd. 
40  yd. 


h.  72  yd. 
50  yd. 
44  yd. 


2.  Find  the  cost  of : 


a.  24  yd. 
16  yd. 
32  yd. 


h.  78  yd. 
69  yd. 
81yd. 


3.  Find  the  cost  of 


a,  100  yd. 
120  yd. 
150  yd. 


5.  108  yd. 
135  yd. 
144  yd. 


90  yd. 
20  yd. 
25  yd. 


e.  12  yd. 
36  yd. 
42  yd. 


160  yd. 
180  yd. 
128  yd. 


d.  75  yd. 
84  yd. 
54  yd. 


d.  92  yd. 
21yd. 
46  yd. 


d.  200  yd. 
240  yd. 
300  yd. 


e.  48  yd. 
96  yd. 
64  yd. 


e.  15  yd. 
18  yd. 
10  yd. 


e.  320  yd. 
400  yd. 
860  yd. 


ALIQUOT   PAETS 

WRITTEN   REVIEW   EXERCISE 


149 


Name 

Quan- 
tity 

PRICE.S 

1 

2 

3 

4 

5 

6 

Boucle  Stripe 

yd- 

$0.10i 

$0.11 

$0.10 

$0,111 

$0.12 

$0.12^ 

Dress  Silks 

yd- 

1.20 

1.25 

1.331 

1.371 

1.40 

1.50 

English  Serge 

yd- 

1.331 

1.30 

1.35 

1.25 

1.37i 

1.45 

Fancy  Gingham 

yd. 

.061 

.06 

.061 

.07 

.07^ 

.071 

Fancy  Plaids 

yd. 

.311 

.32 

.33^ 

.35 

.34 

.37i 

Gunner's  Duck 

yd. 

.14 

.15 

.IH 

.16 

.17 

.17i 

Percale  Shirting 

yd. 

.07 

.07^ 

.08 

.08^ 

.09 

.09^ 

Scotch  Cheviot 

yd. 

.39 

.40 

.37i 

.45 

.44 

.48 

Taffeta  Silk 

yd. 

.871 

.85 

.90 

.88 

.921 

.95 

Wash  Silk 

yd. 

.30 

.37i 

.40 

.35 

.42 

.4H 

Prepare  each  of  the  following  invoices  in  correct  form,  omit  the 
heading,  and  find  the  value  hy  each  price  list. 


5. 


22  yd.  Boucle  Stripe 
27  yd.  English  Serge 
56  yd.  Percale  Shu^ing 
48  yd.  Wash  Silk 

2.    72  yd.  Dress  Silk 
104  yd.  Scotch  Cheviot 
64  yd.  Taffeta  Silk 
60  yd.  Gunner's  Duck 

36  yd.  Fancy  Gingham 
88  yd.  Scotch  Cheviot 
92  yd.  Wash  Silk 
20  yd.  Boucle  Stripe 
80  yd.  Gunner's  Duck 

4.    96  yd.  Fancy  Plaids 
36  yd.  English  Serge 
100  yd.  Taffeta  Silk 
70  yd.  Percale  Shirting 
90  yd.  Wash  Silk 

72  yd.  Boucle  Stripe 
56  yd.  Wash  Silk 
50  yd.  Fancy  Plaids 
80  yd.  Dress  Silk 
70  yd.  Gunner's  Duck 

6.    84  yd.  Taffeta  Silk 
QQ  yd.  Fancy  Gingham 
84  yd.  Scotch  Cheviot 
^Q  yd.  EngHsh  Serge 
45  yd.  Percale  Shirting 

CHAPTER   XI 

BILLS  AND  ACCOUNTS 
BILLS 

172.  A  detailed  statement  of  goods  sold,  or  of  goods  bought 
to  be  sold,  is  called  either  a  bill  or  an  invoice.  A  detailed  state- 
ment of  goods  bought  to  be  used  or  consumed,  such  as  office 
furniture,  stationery,  and  fuel,  or  a  statement  of  services  ren- 
dered, or  of  a  work  performed,  is  called  a  bill. 

Thus,  a  physician's  statement  of  services  rendered,  or  a  transportation 
company's  bill  for  work  performed,  and  the  charges  for  the  same,  is  called  a 
hill;  but  a  statement  of  a  quantity  of  silk  bought  or  sold  by  a  dry-goods 
merchant  in  the  course  of  trade  is  called  either  a  hill  or  an  invoice. 

173.  The  models  following  show  a  variety  of  current  prac- 
tices in  billing.    They  will  therefore  be  found  helpful  as  studies. 

1.   Groceries 
Boston,  Mass.,         Oct.    15,         19 

Messrs.   SMITH,    PERKINS  &  CO. 

Rochester,    N.Y. 

Bought  of  E.  E-  GRAY  COMPANY 

Terms  30  da.  Telephone,  Main  167 


3 

10 
5 


bbl.  Rolled  Oats  $6.25 

"   Gold  Medal  Flour       6.50 

bx.  Wool  Soap  3.10 


18 
65 
15 


75 

00 
50 


99 


25 


This  is  one  of  the  simplest  bill  forms;  it  is  the  form  that  is  common 
in  a  great  many  lines  of  business. 

160 


BILLS  AND  ACCOUNTS 


151 


2.   Groceries 

Boston,  Mass.,         Nov.    12,  19 

Messrs.    E.    0.    Sherman  &  Co. 

Charlestown,   Mass. 

Bought  of  S.  S.  PIERCE  COMPANY 

Terms  50  da.;  5fo  10  da. 

10  Red  Label  Hams      146  lb.   $0.,23   $33.58 
20  mats  Java  Coffee   1500  ^  .25   375.00 

12  6-lb.  tins  Mustard   72   "     .36   25.92 
15  6-lb.  tins  Cocoa     90   "     .34   30.60 

$465.10 

Goods  bought  by  the  mat,  chest,  case,  etc.,  are  frequently  billed  by  the 
pound.     The  above  bill  shows  the  form  in  such  cases. 


3.   Hardware 

The  following  bill  is  sometimes  used  in  the  hardware  business.  The  first 
number  after  the  name  of  the  article  is  the  quantity ;  the  number  above  the 
horizontal  line  following,  the  price ;  and  the  number  below  the  line,  the 
grade.  Thus  the  first  item  in  the  bill  shows  that  12  doz.  porcelain  knobs  in 
all  were  sold,  of  which  6  doz.  were  No.  8  at  $1.25  and  6  doz.  No.  16  at  $1.33  J. 


^ew  york. 


19- 


bought  of  J^/ie  Eureka  jrtareiL 


e. 


ompanif 


ZS 


152 


CONCISE   BUSINESS  ARITHMETIC 


4.   Wholesale  Dry  Goods 


^    >o     CHICAGO. /^Z^^^4^.  Ar;  10 


Bought  of  MARSHALL  FIELD  &  CO. 

Franklin  Street  and  Fifth  Avenue 


j^i. ^J    ^/'    ^^^    ^o'  ^s.'- s-gg. 


JJLJL 


J-2:. 


^ 


3  Z^     ^^^    JA/'-    3e?'    ^O' 


J6^ 


^ 


2^ 


^ 


/^^ 


1J=. 


^o     Jf     ^Z.     ^o     ¥^i.     ^o 
¥'i.     ^/      ACi.       ^/      <^^       iA3 


A^jT  ^^{    ZA/ 


ZJL 


/3X 


±2^ 


!/      ^3     %^2.     4^V      ^S      Jf 


/^7 


L2=. 


'  y/  •»         Zl  /I       U-/0        ZAO        //..^       ^Of^ 


¥ft  J//2^ 


/rC^TJL 


^2.      ¥0      4^      ^O       ^J     3^^ 
^/      ^3     ^C     ^^     ¥^    ^^^ 


jik 


j^ 


^ 


/.^^ 


X 


-fo^^^r^y^^ 


l^y^Z^ii^-p^.^1^4^^^^ 


37     ¥/    3f^  A^/  ^  37    4<a 


Z^^    //i 


JLJL 


/^/ 


~i^<^rc//Arl^.^t?-7^7:6- 


In  the  wholesale  dry-goods  business  the  price  is  generally  for  a  yard, 
and  the  number  of  yards  to  the  piece  varies  in  some  kinds  of  cloth.  The 
first  item  in  the  above  bill  is  followed  by  a  series  of  numbers,  41,  42,  etc. ; 
these  represent  the  number  of  yards  in  each  of  the  12  pc.  Immediately 
following  these  numbers  is  recorded  the  total  number  of  yards  in  the  12  pc. 
The  total  number  of  yards  should  be  found  by  horizontal  addition. 

5.   Manufactueer's 

The  following  is  a  bill  for  neckwear.  The  different  styles  are  distin- 
guished by  the  marks  at  the  left  of  the  quantity.  This  form  is  common 
among  manufacturers,  jobbers,  and  wholesalers.  Bills  on  which  trade 
discounts  (see  page  188)  are  allowed  are  arranged  as  shown  in  this  bill. 


BILLS  AND  ACCOUNTS 

JQetogorlt,       Oct.   10,        19 

JHessrs.    J.   E.   Whiting  &  Co. 

Boston,   Mass. 

25ougf)t  of  S^o^n^on  25tD^.,  ^on$  a  Co. 

Ccrmfi  Net  30  da. 


153 


721 

n 

doz.  Neckwear 

$4.50 

6 

75 

1026 

1 

2 

27.00 

13 

50 

1025 

n 

27.50 

41 

25 

1020 

3 
4 

9.00 

6 

75 

923 

2| 

18-00 

45 

00 

1015 

n 

24.00 

42 

00 

155 

25 

Less  255 

3 

11 

152 

14 

1 

6.   Furniture 

In  the  following  bill  the  goods  were  sold  delivered  on  the  cars  (f.  o.  b.) 
Boston,  but  the  shippers  prepaid  the  freight  to  Bangor.  The  freight  is  a 
part  of  the  selling  price  and  is  added  to  the  amount  of  the  bill,  as  shown 
in  the  model. 


BOSTON,. 


M^.AA^^ .U.c^^^^^f^^^ 


6r^Z^  Z3, 19 . 


Ar^^. 


'.^n^f^l^^:^-?^. 


Bought  of  E.   M.   PRAY,  SONS  &  CO. 

AT^  Manufacturers  of  Fine  Furniture 

TERMS  //C^Jff.^-r^^ 


AJIL 


.  ^ 


'^^^.^l.d^^jr^^^YT-r^j'^^ 


JJli 


/2-3 


7^- 


A2^ 

JJL 


^ 


79fayA^fr7^^sz^^^X^^^^. 


Z^ 


^ 


'>ry-7^y7.^f:7^2^. 


fy^^  /7^ 


/7^ 


>r:T^^^ 


/a^ 


ZAA 


s^ 


'J37 


^^^^U^S-t^yA 


J^ 


/o 


'J^± 


?^ 


154 


CONCISE   BUSINESS  ARITHMETIC 


7.   Wholesale   Coal 
F.  H.  OSBORN  &  CO. 

SHIPPERS  OF 

Anthracite,   Bituminous,  and  Gas  Coal 


Sold 


Temi£ 


ana 


Boston,. 


.19_ 


/^  Z  ^^^^^^^V./Tg7^--^4^  ^^^^^ 


'?^'7 rn n  ^-V^^^^ 


A^^So_ 


lA^J2j2jtl!^^:=t^ 


jjll 


Ay 


z^ . 


ta^CPC 


>r7-t^~£^ 


jJH 


vu 


T-fyoo  ^^^^.^^^J? 


JA^ 


l^ 


7-^/ 


^^ 


"/fe^  ^.^o^/-e.^-^^2''PC^^C''-y^  ^.^y?.^ 


-^^=^n47^^.re^ 


^^^r^ 


The  above  is  the  form  of  bill  generally  used  for  wholesale  transactions 
in  coal.  It  is  called  a  receipted  bill,  and  shows  that  the  coal  has  been  paid  for. 


8.   Retail  Coal 


CermB- 


T 


JL 


2  -T;^777^<7^-A<:^;>^r7VJ^'-^^^^;>.g:7^ 


^j^ff-z/^Ao   i<jj>^-^/l^       Faaff#-    ^^ 


J=^ 


2^ 


IjL 


2.  -i>r?~x:?^^  ■^^^<f'^yy^^..^y-z^yL 


/^JS'fP- 2/A^(7    (,a^o-2./A^^    /-^g^/^#      /i^- 


2.^ 


J-g 


^o 


/^^r</<~^ 


^m^^^l^^Z- 


^^-/.(/^U\ 


BILLS  AKD  ACCOUNTS 


155 


The  foregoing  bill  shows  a  form  sometimes  used  by  retailers.  The 
numbers  at  the  left  of  the  hyphen  are  the  gross  weights,  and  the  numbers 
at  the  right  the  tares  of  the  different  loads. 


9.   China   and   Glassware 

t/joston,  Nov.  6,  f9 

^^  THE  WENTWORTH  =  STRATTON   CO. 

Rochester.   N.Y. 

bought  of  (Osgood,   fJ^ raver  &*  C^on 

%/erms  60  da.   net;   2%  10  da. 


25 


Dinner 

Set,  130  pieces;  viz. : 

1  doz. 

Plates.  8  in. 

1  " 

7  .. 

1  " 

6  " 

1  •• 

7  ••  (deep) 

1  '*   Fruit  Saucers,  4  in. 

1  " 

[ndividual  Butters 

1/12  doz.  Covered  Dishes.  8  i 

1/12   ' 

'   Casseroles,  8  in. 

1/4    • 

'  Dishes,  8  in. 

1/12   ' 

10  " 

1/3  2   • 

12  " 

1/12   • 

14  *• 

1/6    * 

•   Bakers,  8  in. 

1/12   ' 

'   Sauce  Boats 

1/12   • 

'   Pickles 

1/12   • 

'   Bowls 

1/12   ' 

Sugars 

1/12   ' 

Creams 

1 

Handled  Teas 

1/2    • 

Coffees 

1/12   ' 

•   Pitchers 

1/12   • 

'   Covered  Butters  and 

Drainers 

more  Di 

nner  Sets  as  above 

Crates 

1 

88 

1 

63 

1 

38 

1 

63 
75 
50 

$12.00 

1 

00 

13.50 

1 

13 

2.50 

63 

4.50 

38 

7.50 

63 

10.50 

88 

4.50 

75 

4.00 

33 

3.00 

25 

2.00 

17 

6.00 

50 

2.79 

2 

23 
00 

2.33 

1 

17 

6.00 

50 

9.00 

75 

19 

07 

19.07 

476 

495 

7 

75 
82 
50 

2 

10 

505^ 

42 


The  above  form  is  common  in  the  china  and  glassware  business.  In  this 
case  a  charge  is  made  for  the  crates  used  in  packing  and  the  prices  do  not 
include  delivery.  The  cost  of  the  crate  and  the  cost  for  carting  are  there- 
fore made  a  part  of  the  bill. 

CB 


156  CONCISE   BUSINESS   AKITHMETIC 

10.    Lumber 
Jhe  7{.  w^.  ^ickford  60. 

SBosfon,  >^Atass,,  0  C  t .    8  ,  /9 

Sold  to   L .  A .  Hammond  &  Co . 

Paterson,  N.J. 

^erms  Pgt .    net   cash;    bal.    in  5  da.    less   I2' 


23,289  ft.  1  X  2j  #1  N.  C.  Ceili 

ng 

$18.50  $430.85 

3,520  "    "     2  "  "    " 

17.00   59.84 

10,307  "  i  X  2l  1  "  "    " 

13.50  139.14 

1,690  "    "     2  "  "    " 

12.50   21.13 
$650.96 

Less  freight  (45,200  lb. 

at  24^)   108.48 

$542.48 

Lumber  is  generally  sold  by  the  thousand  feet.  In  the  above  bill  the  goods 
were  sold  free  on  board  cars  (f.  o.  b.)  Paterson,  N.J.,  but  the  shippers  have 
not  prepaid  the  freight.  They  find  that  these  charges  are  %  108.48  and  deduct 
this  amount  from  the  total  of  the  bill.  In  the  wholesale  lumber  business  the 
prices  quoted  usually  include  the  cost  of  delivery,  and  when  the  freight  charges 
are  not  known  at  the  time  of  making  the  shipment,  they  are  paid  by  the 
consignees  and  deducted  from  the  amount  of  the  bill  on  the  arrival  of  the 
goods.     The  freight  bill  is  then  sent  to  the  shippers  for  credit. 

WRITTEN  EXERCISE 

1.  Study  the  model  bill,  page  150.  Increase  the  price  of 
each  article  25;^  and  then  copy  and  find  the  amount  of  the  bill. 

2.  Study  the  first  model  bill,  page  151,  and  then  copy  and  find 
the  amount  of  it  at  the  following  prices:  hams,  27)^;  coffee, 
23^;  mustard,  31)^;  cocoa,  39)^. 

3.  Study  the  second  model  bill,  page  151,  and  then  copy  and 
find  the  amount  of  it  at  the  following  prices :  porcelain  knobs 
#8,  $1,121;  #16,^1.25;  steelyards  #64,  $11;  #17,  $8.33J; 
jack-planes  #14,  $6;  #21,  16.25;  #48,  $6.75. 


BILLS  AND  ACCOUNTS  157 

4.  Apr.  15,  you  bought  of  S.  S.  Pierce  Co.,  Boston,  Mass., 
for  cash;  25  gal.  finest  New  Orleans  molasses  at  48^;  15  gal. 
fancy  sugar-house  sirup  at  49^;  75  lb.  raw  mixed  coffee  at 
29^;  25  lb.  raw  Pan-American  coffee  at  19/;  5  cartons  Fowle's 
entire-wheat  flour  at  39|/;  |^bbl.  Franklin  Mills  flour  at  $6.75; 
J  bbl.  pastry  flour  at  15.25.     Write  the  bill. 

5.  Mar.  19,  Frank  M.  Richmond  &  Co.,  New  York  City, 
sold  to  Charles  M.  Thompson,  Poughkeepsie,  N.Y.,  12  doz.  por- 
celain knobs:  3  doz.  #71  at  $6.35,  9  doz.  #74  at  16.75;  12 
doz.  shingle  hatchets:  6  doz.  #16  at  $9.75,  6  doz.  #34  at 
$12.50;  7  doz.  steel  squares:  3  doz.  #91  at  $35,  4  doz.  #73 
at  $33.     Terms:  30  da.     Write  the  bill. 

6.  Study  the  model  bill  on  page  152.  Increase  the  prices 
of  the  articles  marked  124  and  132  five  cents  each  and  the  re- 
mainder of  the  articles  one  cent  each;  then  copy  and  find  the 
amount  of  the  bill. 

7.  Nov.  15,  J.  B.  Ford  &  Co.,  Albany,  N.Y.,  bought  of  the 
Clinton  Mills,  Little  Falls,  N.Y.,  10  pc.  percale  shirting  con- 
taining 42, 48, 521, 58^  62,  38, 49, 51, 54,  and 46^ yd.,  at  7|  / ;  10  pc. 
fine  wool  cheviot  containing  58^,  42,  49,  51,  442,  45^  43,  412^  39, 
and  42  yd.,  at  $1.12J;  5  pc.  cashmere  containing  49^,  40^,  48^, 
491,  and  49  yd.  at  $1.37^.  Terms:  60  da.,  or  3%  discount 
for  cash  within  10  da.     Write  the  bill. 

8.  Study  the  first  model  bill  on  page  153.  Increase  the 
prices  of  styles  1026,  1025,  1020,  and  923,  25/  each  and 
diminish  the  prices  of  the  other  styles  25^  each;  then  copy 
and  find  the  amount  of  the  bill.    Omit  the  discount. 

9.  Sept.  24,  Geo.  W.  Fairchild,  Buffalo,  N.Y.,  bought  of 
E.  M.  Lawrence  &  Co.,  New  York  City,  silk  ribbon  as  follows : 
12  pc.  #1142  at  $2.25;  5  pc.  #1321  at  $1.25;  25  pc.  #171 
at  $4,371;  8  pc.  #  1927  at  $1.75;  36  pc.  #2114  at  $1.66|;  15 
pc.  #1371  at  $1,331;  15  pc.  #624  at  $4.371 ;  12  pc.  #909  at 
$L87l;  25  pc.  #1008  at  $3,331;  25  pc.  #1246  at  $4.75;  18 
pc.  #2119  at  $1,121  Terms:  30  da.,  or  2%  discount  for  cash 
in  10  da.     Write  the  bilL 


158  CONCISE   BUSINESS   ARITHMETIC 

10.  Study  the  second  model  bill  on  page  153.  Increase  the 
price  of  the  articles  marked  65  and  396,  25^  each,  and  diminish 
the  price  of  the  other  articles  i2|^  each;  then  copy  and  find 
the  amount  of  the  bill.     Freight  added,  '$14.70. 

11.  July  20,  The  Hayden  Furniture  Co.,  Rochester,  N.Y., 
bought  of  John  H.  Pray  &  Son,  Boston,  Mass.,  25  #31  card 
tables  at  $11;  21  #94  china  closets  at  $2T.50;  15  #16  dining 
sets  at  $85;  25  #3060  fancy  rockers  at  $9.25;  15  #35  music 
cabinets  at  $2.75;  25  #26  mahogany  office  chairs  at  $12.50; 
12  #89  oak  sideboards  at  $125.  Terras:  30  da.  The  prices 
are  free  on  board  Boston,  and  the  shipper  prepaid  the  freight, 
134.50.     Write  the  bill. 

12.  Study  the  first  model  bill  on  page  154.  Increase  the 
price  of  the  stove  coal  25^  per  ton  and  the  price  of  each  of  the 
other  kinds  12|^^  per  ton;  then  copy  and  find  the  amount  of 
the  bill.     Receipt  the  bill  for  F.  H.  Osborn  &  Co. 

13.  May  19,  C.  E.  Williams  &  Co.,  Cleveland,  O.,  bought  of 
Fairbanks  &  Co.,  Scranton,  Pa. :  3  car  loads  of  stove  coal  weigh- 
ing 20,500,  26,400,  and  25,600  lb.,  respectively,  at  $4.75  per  ton 
(2000  lb.);  1  car  load  grate  coal  weighing  21,900  lb.  at  $4.25  per 
ton;  1  car  load  cannel  coal  weighing  22,500  lb.  at  $7.75  per 
ton.  Terms:  30  da.,  or  3%  discount  for  cash  in  10  da.  Write 
the  bill. 

14.  Study  the  second  model  bill,  page  154,  then  copy  and 
find  the  amount  of  it  at  $6.25  per  ton  for  each  sale. 

15.  Copy  the  bill  in  problem  14  in  accordance  with  the  model 
shown  on  page  154.     Make  the  price  of  the  coal  $6. 66 J. 

16.  Study  the  model  bill  on  page  155.  Increase  each  price 
given  five  cents  and  then  copy  and  find  the  amount  of  the  bill. 
Cost  of  crates  used  in  packing,  $6.40 ;  carting,  $2.80. 

17.  July  15,  Henry  Nelson  &  Co.,  Portland,  Me.,  bought  of 
Jones,  Stratton  &  Co.,  New  York  City,  5  doz.  plates,  8  in.,  at 
$1.50;  35  doz.  plates,  7  in.,  at  $1.35;  15  doz.  plates,  6  in., 
at  $1.10;  10  doz.  plates,  5  in.,  at  90/ ;  65  doz.  handled  teas  at 
$1.85.  Terms:  30  da.  Cost  of  crate  used  in  packing,  $2; 
cartage,  75/.     Write  the  bill. 


BILLS  AND  ACCOUNTS 


159 


PAY  ROLLS 

PAY    ROLL  For  th>.  wi.^V  ^nHing    ^-^^A^A  /^       Tg 


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This  form  is  most  common  among  manufacturing  establishments,  but 
it  is  also  used  by  printers,  contractors,  and  builders. 

Checks  are  sometimes  used  in  paying  off  employees,  but  most  large  con- 
cerns find  the  envelope  system  the  most  convenient  and  satisfactory.  To 
pay  off  employees  by  the  envelope  system  it  is  necessary  for  the  bookkeeper 
to  find  first  the  amount  of  money  required  and  then  the  bills  and  fractional 
currency  that  are  necessary  to  pay  each  employee.  The  amount  required  is 
the  total  of  the  pay  roll,  and  the  bills  and  fractional  currency  desired  may 
be  found  as  shown  in  the  following  illustration.  This  illustration,  called 
a  change  memorandum,  shows  the  method  of  finding  just  the  denominations 
wanted  for  the  j^ay  roll  at  the  top  of  the  -page.  A  change  memorandum 
may  be  proved  correct  as  shown  in  the  pay-roll  memorandum  at  the  top  of 
page  160. 


No 

Bills 

Coins 

$20 

$10 

$5 

$2 

$1 

mf 

^f 

10^ 

hf 

\f 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

1 

1 

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1 
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1 

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1 

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3 

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7 

5 

6 

5 

6 

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9 

160 


CONCISE   BUSINESS    ARITHMETIC 


FIRST  NATIONAL  BANK 

Westfield,  Mass. 

PAY-ROLL  MEMORANDUM 

NELSON  y  CO. 

require  the  following: 


When  the  amount  of  the  j)ay  roll 
and  the  necessary  bills  and  frac- 
tional currency  have  been  deter- 
mined, a  check  payable  to  the  order 
of  Pay  Roll  is  written.  A  pay-roll 
memorandum  similar  to  the  accom- 
panying form  is  then  attached  to 
the  check  and  both  are  sent  to  the 
bank.  The  pay-roll  memorandum 
should  foot  the  same  as  the  pay- 
roll book,  and  is  therefore  a  check 
upon  the  correctness  of  the  change 
memorandum. 

*  In  a  large  pay  roll  the  adept 
bookkeeper  frequently  estimates  the 
kind  of  change  required.  This  is 
done  by  scanning  the  pay  roll  first 
to  find  the  number  of  pennies  re- 
quired, then  the  number  of  nickels, 
etc.    The  experienced  bookkeeper  can  make  a  very  accurate  estimate 


Pennies 'f 

Nickels ^ 

Dimes ^ 

Quarters     .......  t/" 

Halves ^ 

Dollars ^ 

a's    . 7 

5's ^ 

lo's 7 

20's Z 


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PAY  ROLL 

For  the 

week  ending- 



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Time  in  hours 

Tot.l 
time 

Rate 

per 

Amount 
advanced 

Amount 
due 

Bills  and  silver  necessary 

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WRITTEN    EXERCISE 


1.  Study  the  model  pay  roll,  page  159,  and  find  the  amount  of 
it  at  the  following  wages  per  hour:  #1, 18/ ;  #2,  21|/;  #3,  25/; 
#4,35/;  #5,331/;  #6,35/;  #7,37i^;  #8,35/;  #9,  27^/; 
#10,  18|/.     Make  a  change  memorandum. 


BILLS  AND  ACCOUNTS 


161 


2.  Study  the  model  pay  roll  on  page  160,  and  then  find  the 
amount  of  it  at  the  following  wages  per  hour:  #1,  50^;  #2,  45^; 
#3,  331^;  #4,  35^;  #5,  27|-^;  #6,  371^;  #7,  25^;  #8,  331 J^;  #9, 
44|^;  #10,22f^;  #ll,22f^;  #12, 14f  ^;  #13,121^;  #14,30)^. 

3.  Make  a  pay  roll  memorandum  from  problem  2. 

WRITTEN   REVIEW   EXERCISE 

1.    Find  the  amount  of  each  of  the  following  bills : 

New   York^  May  31,  /p 

ATessrs.  Gray,  Salisbury  &  Co. 

Rochester,  N.Y. 

Bought  of  y.   E.   PAGE,   SONS  &  CO. 


Terms 

;  net, 

60  da.;  2%  10  da. 

Cask 

Pieces 

Dksceiption  op  Aeticlbs 

Yds. 

Price 

Items 

Amount 

#364 

10 

Velveteen 
421  40    40    46    38i 
40    42    42    41     39 

25^ 

#359 

12 

Corduroy 

36  381  392  42    412  392 

37  37    41    45    41    40i 

66f^ 

#371 

15 

Gray  Homespun 
39    38    35    42    41 
45    39    41    34    37 
41     40    41     38    423 

83  J  ^ 

#360 

6 

Storm  Serge 
40    421   43    42    39    421 

44^ 

#373 

24 

Fine  English  Serge 
42    38     42    42    402  421 
40    39    40    41    401  43 

42  42     382  38    4I    42 

43  44    41    40    371  37 

1.371 

#381 

24 

Groveland  Flannel 
32    40    39    42    41     45 
45    46    35    41    38    41 
37    42    43    40    37    42 
37    40    42    41    44    41 

33i 

162  CONCISE    BUSINESS   AEITHMETIC 

2.  Make  out  a  bill  for  the  following  order.  Bill  the  English 
breakfast  tea  at  41 J^ ;  Finest  oolong  tea  at  65^;  Young  Hyson 
tea  at  97^^;  Choice  Japan  tea  at  59^;  Orinda  kaughphy  at 
11.90;  raw  Java  coffee  at  30^^;  gluten  flour  at  30^  a  carton 
and  87.75  per  barrel.  Assume  that  half  a  chest  of  tea  weighs 
75  lb.,  and  a  mat  of  coffee  70  lb. 

E.   M.  BARBER  &  SON 

RETAIL  GROCERS 
Springfield,  Mass.,         Aug .  13 ,  19 

S.  S.  Pierce  Company 

Boston,  Mass, 

Gentlemen: 

Please  ship  us  via  B.  &  A.  R.R.,the  follow- 
ing goods: 

3  hf.  cht.  English  Breakfast  Tea 

3  "    "   Finest  Oolong  Tea 

5  "    "   Young  Hyson  Tea 

25  lb.  Choice  Japan  Tea 

5  5-lb.  cans  Orinda  Kaughphy 

7  mats  Raw  Java  Coffee 

5  hf.  bbl.  Gluten  Flour 

25  5-lb.  cartons  Gluten  Flour 

Respectfully  yours 

3.  Boston,  Mass.,  Apr.  16,  E.  O.  Burrill,  Philadelphia,  Pa., 
bought  of  Jones,  Talcott  &  Co.,  on  account,  30  da.,  25  Turk- 
ish rugs  41  X  7  at  $10.25 ;  750  yd.  matting  at  55^ ;  225  yd.  lin- 
oleum at  271^;  25  Turkish  rugs  81  x  12  at  $21.75;  25  Persian 
rugs6  x9at  $12.25;  12  Persian  rugs  7  x  11  at  $16.25;  10  rolls, 
each  containing  150  yards,  Brussels  carpeting  at  $2.25 ;  275  yd. 
Moquette  carpeting  at  $1.75.     Find  the  amount  of  the  bill. 


BILLS  AND   ACCOUNTS 


163 


TIME  SLIP 

TIME  SLIP 

Friday,    4/26,   19 

— 

Saturday,    4/27,    19— 

IN 

OUT 

IN 

OUT 

IN 

OUT 

IN 

OUT 

1 

751 

1201 

1256 

502 

1 

753 

1200 

1258 

502 

2 

747 

1202 

1247 

503 

2 

757 

1204 

1259 

501 

3 

744 

1204 

1254 

504 

3 

753 

1200 

1256 

504 

4 

751 

1205 

1255 

501 

4 

755 

1202 

1254 

502 

5 

753 

1206 

1259 

505 

5 

749 

1201 

1257 

504 

6 

751 

1202 

1259 

503 

6 

828 

1203 

1255 

503 

7 

859 

1201 

1254 

502 

7 

755 

1202 

1253 

501 

8 

756 

1202 

1250 

501 

8 

857 

1201 

1254 

502 

9 

757 

1201 

1259 

502 

9 

758 

1202 

1258 

504 

The  above  slips  show  a  record  of  time  for  9  employees  for  2  da.  in  a 
large  printing  establishment.  The  records  are  made  by  a  large  mechani- 
cal timekeeper,  and  at  convenient  periods  are  copied  in  the  pay-roll  book. 
Fractions  are  recorded  to  the  nearest  i  of  an  hour.  The  above  record  is 
based  on  an  eight-hour  day,  from  8  to  12  a.m.,  and  1  to  5  p.m.  If  a  record 
is  made  before  the  hour  for  beginning  work,  either  in  the  morning  or  at 
noon,  it  is  not  counted  in  the  regular  time,  but  if  an  employee  is  late,  his 
record  for  time  begins  at  the  nearest  multiple  of  ten  after  the  record  is 
made.  For  instance,  if  an  employee  rang  in  at  8:42  a.m.,  his  time  for  the 
morning  would  begin  at  8:50.  In  the  above  slip  for  Friday,  No.  1  rang 
in  at  7:51  and  left  at  12:01;  he  rang  in  at  12:56  and  rang  out  at  5:02; 
time,  8  hr. 

4.  Copy  the  following  pay  roll,  enter  the  time  for  Friday  and 
Saturday  (from  the  above  slips),  find  the  amount  of  the  pay  roll ; 
make  a  change  memorandum  and  a  pay-roll  memorandum. 


PAY  ROLL 

For  the  Wee 

K  Ending 

April 

27, 

19— 

No. 

Name 

Number  of  Hours' 
Work  Each  Day 

Total 
No.  OF 

Wages 

PER 

Total 

Remarks 

M. 

T. 

W. 

T. 

F. 

S. 

Hours 

Hour 

1 

A.  B.  Comer 

8 

8 

8 

8 

55^^ 

2 

W.  D.  Ball 

8 

8 

8 

8 

A^^ 

3 

A.  M.  Snow 

8 

8 

8 

8 

U^f 

4 

R.  0.  Mark 

8 

8 

8 

8 

334)? 

5 

Miss  Mary  Cane 

8 

7| 

8 

8 

33^,? 

6 

Miss  Ellen  Kyle 

8 

7^ 

8 

8 

35^ 

7 

D.  M.  Garson 

8 

I:- 

8 

8 

S6ft 

8 

S.  D.  Lane 

8 

n 

n 

8 

25/ 

9 

Miss  Cora  Knapp 

8 

8 

n 

8 

221/ 

164 


CONCISE   BUSINESS    AEITHMETIC 


EXPKESSAGE   AND   EREIGHTAGE 

These  express  rates  went  into  effect  February  1, 1914,  in  con- 
formity with  the  order  of  the  Interstate  Commerce  Commission : 


Bktween  New  York 

Between  New  York 

Between  New  York 

AND  Chicago 

AND  New  Orleans 

AND  Denver 

1st  class     2d  class 

1st  class 

2d  class 

1st  ela^ts 

2d  class 

51b.  31/ 

31/ 

41/ 

41/ 

47/ 

47/ 

6       33 

32 

46 

46 

53 

53 

7      35 

32 

50 

48 

58 

57 

8       38 

32 

54 

48 

64 

57 

9       40 

32 

59 

48 

69 

57 

10       42 

32 

63 

48 

75 

57 

15       53 

40 

84 

63 

1.02 

77 

20       64 

48 

1.06 

80 

1.30 

98 

25       75 

57 

1.27 

96 

1.57 

1.18 

Between  Chicago 

Between  Chicago 

Between  Chicago 

AND  Boston 

AND  Galveston 

AND  Portland,  Ore. 

1st  class     2d  class 

1st  class 

2d  class 

1st  class 

2d  class 

5  lb.  31/ 

31/ 

39/ 

39/ 

63/ 

63/ 

6       34 

33 

43 

43 

72 

72 

7       36 

33 

47 

45 

81 

80 

8       38 

33 

51 

45 

89 

80 

9       41 

33 

55 

45 

98 

80 

10       43 

33 

59 

45 

1.06 

80 

15       54 

41 

78 

59 

1.50 

1.13 

20       Q6 

50 

98 

74 

1.93 

1.45 

25       77 

58 

1.17 

88 

2.36 

1.77 

Under  the  new  system  the  country  is  divided  into  blocks,  each  block 
covering  a  certain  designated  territory,  and  fixed  rates  are  made  for  certain 
weights  and  distances,  not  as  under  the  old  system,  at  so  much  per  pound. 

The  tables  given  herewith  suggest  the  manner  in  which  charges  are 
made  for  given  amounts  to  certain  points. 

First-class  matter  includes  all  merchandise ;  second-class  matter  applies 
to  food  and  drink,  and  these  terms  are  elaborated  and  explained  in  the 
instructions  to  express  agents.  On  small  packages  the  difference  in  charges 
for  first-class  matter  or  second-class  matter  is  very  slight  (sometimes  the 
same),  but  for  large  packages  and  long  distances  the  difference  is  marked. 


BILLS   ANB   ACCOUKTS 


165 


WRITTEN  EXERCISE 

1.  Find  the  total  cost  of  sending  the  following  packages 

10  lb.  first  class  from  New  York  to  Chicago. 
5  lb.  second  class  from  Chicago  to  Boston. 
15  lb.  first  class  from  Chicago  to  Galveston. 
20  lb.  second  class  from  New  York  to  Denver. 
10  lb.  first  class  from  New  York  to  New  Orleans. 

2.  Find  the  total  cost  of  sending  the  following  packages 

15  lb.  first  class  from  Chicago  to  Galveston. 

25  lb.  second  class  from  Chicago  to  Portland,  Ore. 

7  lb.  second  class  from  Boston  to  Chicago. 

9  lb.  first  class  from  Chicago  to  New  York. 
10  lb.  first  class  from  Galveston  to  Chicago. 

3.  Find  the  amount  of  the  following  freight  bill  : 


Date  of  W.  B.AU^^/^ig       W.  B.  No.  ^Cyf  Albany y  N.Y.A^cOyZo/^ 

To  The  Interstate  Transportation  Company,  Dr, 

For  Transportation  frorn^^t:^iit^:mo  ^^-^^-2:1^^7^^ 


Weight 


>  /  /  /^        ZjT^ 


Advance  charges 
Received  paymen. 


No.  CarJ//A^J- 


Freight  Agent 


/J- 


P  ? 


Bulky  goods  are  generally  sent  by  freight.  The  articles  are  divided, 
according  to  quantity  and  character,  into  different  classes  and  are  subject 
to  different  rates.  All  railroads  follow  some  official  classification.  All 
official  classifications  divide  freight  into  six  different  classes. 

Such  bulky  articles  as  furniture,  uncased,  is  subject  to  a  classification 
called  double  first-class.  There  is  so  much  unoccupied  space  that  the  first- 
class  rate  is  doubled. 


166 


CONCISE   BUSINESS   ARITHMETIC 


Such  freight  as  organs  and  pianos  in  cases,  furniture,  statuary,  etc.,  is 
generally  designated  as  first-class  matter.  Baled  hay,  iron,  etc.,  in  car  loads, 
is  generally  designated  as  fifth-class  matter.  Building  blocks,  brick,  etc.,  in 
car-load  lots,  is  generally  designated  as  sixth-class  matter.  First-class  rates 
are  the  highest  and  sixth-class  rates  are  the  lowest  charged. 

Between  most  points,  shipments  weighing  less  than  100  lb.  are  charged 
as  100  lb.,  irrespective  of  weight. 

BOSTON   &  ALBANY  EAILEOAD 

Local  Freight  Tariff  between 

BOSTON,  MASS. 


Stations 


So.  Framingham 
Westboro  .  . 
Worcester  .  . 
Webster  .  .  . 
Palmer     .    .     . 


Rate  peb  100  Lb. 


Classes 


2      3      4      5      6 


6f 

If 

9f 

10^ 


5^ 


98 
108 
146 
150 
202 


Stations 


Springfield 
Westfield 
Athol  .    . 
Pittsfield 
Albany    . 


Rate  per  100  Lb. 


Classes 


28^ 
35j? 


20  20^ 
25^120^ 
23^ 


23^ 
25^ 


4      5      6 


IW 


12)^  lOj* 


11^ 
11J2J 
12J^ 


4.  Using  the  table,  find  the  amount  of  freight  to  charge  on 
27,500  lb.  sixth-class  matter,  from  Boston  to  Pittsfield. 

5.  Using  the  above  table,  find  the  amount  of  freight  to 
charge  on  27,290  lb.  sixth-class  matter  and  890  lb.  first-class 
matter  from  Boston  to  Albany ;  to  Westfield. 

6.  Using  the  above  table,  find  the  amount  of  freight  to 
charge  on  14,790  lb.  fifth-class  matter  and  2170  lb.  second-class 
matter  from  Boston  to  Palmer;  to  Worcester;  to  Pittsfield; 
to  Springfield. 

7.  Using  the  above  table,  find  the  amount  of  freight  to 
charge  on  75  lb.  first-class  matter,  125  lb.  second-class  matter, 
1250  lb.  third-class  matter,  7290  lb.  fourth-class  matter,  21,490 
lb.  fifth-class  matter,  and  64,640  lb.  sixth-class  matter  from 
Boston  to  South  Framingham ;  to  Westboro ;  to  Webster ;  to 
Springfield ;  to  Athol ;  to  Albany. 


BILLS   AND   ACCOUNTS  167 


ORAL  REVIEW  EXERCISE 


Each  problem  on  pages  167  and  168  should  he  completed  in 
approximately  four  minutes.     Without  copying^  find  the  cost  of: 


1. 

2. 

3. 

32  yd.  at  61/ 

176  yd.  at  121/ 

149  yd.  at  25/ 

240  yd.  at  81.121- 

177  yd.  at  50/ 

150  yd.  at  $1,331 

25  yd.  at  S2.50^ 

210  yd.  at  28f  / 

120  yd.  at  $1.25 

19  yd.  at  4J/ 

291  yd.  at  33^/ 

169  yd.  at  11/ 

57  yd.  at66|/ 

104  yd.  at  21/ 

162  yd.  at  121/ 

36  yd.  at  31/ 

98  yd.  at  7/ 

48  yd.  at  61/ 

241  yd.  at  8/ 

90  yd.  at  6f  / 

331  yd.  at  9/ 

190  yd.  at  25/ 

45  yd.  at  S  1.331 

174  yd.  at  30/ 

75  yd.  at  28/ 

45  yd.  at  45/ 

291  yd.  at  3/. ' 

75  yd.  at  12 1/ 

706  yd.  at  331/ 

117  yd.  at  9/ 

42  yd.  at  21/ 

221  yd.  at  8/ 

18  yd.  at  31/ 

246  yd.  at  11/ 

146  yd.  at  11/ 

1821  yd.  at  10/ 

48  yd.  at  101/ 

74  yd.  at  12i  / 

179  yd.  at  20/ 

28  yd.  at  6/ 

78  yd.  at  25/ 

64  yd.  at  121/ 

144  yd.  at  121/ 

44  yd.  at  $1.25 

167  yd.  at  50/ 

4. 

33  yd.  at  331/ 

5. 

48  yd.  at  S  1.50 

6. 

688  yd.  at  Sl.lO 

96  yd.  at  371/ 

36  yd.  at  $1.25 

521  yd.  at  10/ 

129  yd.  at  11/ 

55  yd.  at  11/ 

156  yd.  at  25/ 

75  yd.  at  IJ/ 

143  yd.  at  50/ 

85  yd.  at  85/ 

75  yd.  at  75/ 

36  yd.  at  70/ 

144  yd.  at  16f  / 

27  yd.  at  80/ 

55  yd.  at  55/ 

34  yd.  at  90/ 

73  yd.  at  1^  / 

95  yd.  at  30/ 

125  yd.  at  20/ 

Qb  yd.  at  65/ 

112  yd.  at  142/ 

53  yd.  at  25/ 

94  yd.  at  331/ 

47  yd.  at  331/ 

29  yd.  at  66f  / 

63  yd.  at  111/ 

53  yd.  at  331/ 

99  yd.  at  25/ 

139  yd.  at  50/ 

17  yd.  at  66f  / 

88  yd.  at  371/ 

64  yd.  at  621/ 

104  yd.  at  121  / 

176  yd.  at  12 1/ 

98  yd.  at  16|/ 

80  yd.  at  6f  / 

25  yd.  at  25/ 

225  yd.  at  25/ 

77  yd.  at  30/ 

88  yd.  at  9  Jj/ 

67  yd.  at  331/ 

99  yd.  at  40/ 

57  yd.  at  50/ 

168  CONCISE   BUSINESS   ARITHMETIC 


7. 

8. 

9. 

128  yd.  at  11/ 

219  yd.  at  11/ 

65  yd.  at  80/ 

73  yd.  at  60/ 

85  yd.  at  30/ 

83  yd.  at  40/ 

76  yd.  at  60/ 

94  yd.  at  25/ 

145  yd.  at  11/ 

177  yd.  at  11/ 

89  yd.  at  11/ 

63  yd.  at  11/ 

72  yd.  at  11/ 

28  yd.  at  2|/ 

151yd.  at  33 1/ 

270  yd.  at  111/ 

112  yd.  at  61/ 

49  yd.  at  75/ 

36  yd. 'at  11/ 

191yd.  at  50/ 

124  yd.  atSl.25 

185  yd.  at  25/ 

781  yd.  at  10/ 

180  yd.  at  121/ 

225  yd.  at  20/ 

306  yd.  at  331/ 

360  yd.  at  371/ 

39  yd.  atSl.331 

122  yd.  at  21/ 

24  yd.  at  S  1.121 

49  yd.  at  66f/ 

32  yd.  at  si. 75 

165  yd.  at  6f/ 

42  yd.  at  S  2.50 

92  yd.  at  121/ 

175  yd.  at  8/ 

25  yd.  at  $1.10. 

224  yd.  at  7/ 

171yd.  at  11/ 

22  yd.  at  61/. 

240  yd.  at  21/ 

132^  yd.  at  10/ 

125  yd.  at  36/ 

276  yd.  at  11/ 

110  yd.  at  25/ 

108  yd.  at  9/ 

68  yd.  at  8/ 

51yd.  at  121/ 

216  yd.  at  121/ 

125  yd.  at  12/ 

301yd.  at  25/ 

10. 

11. 

12. 

62  yd.  at  41/ 

144  yd.  at  871/ 

97  yd.  at  30/ 

189  yd.  at  111/ 

25  yd.  at  S  1.62 

36  yd.  atS1.16f 

78  yd.  at  40/ 

14  yd.  at  S  1.14  2 

225  yd.  at  8/ 

334  yd.  at  7/ 

612  yd.  at  6/ 

1431  yd.  at  4/ 

255  yd.  at  5/ 

1171yd.  at  10/ 

65  yd.  at  101/ 

78  yd.  at  11  / 

45  yd.  at  11/ 

15  yd.  at  If/ 

118  yd.  at  11/ 

155  yd.  at  12/ 

235  yd.  at  20/ 

187  yd.  at  25/ 

247  yd.  at  50/ 

66  yd.  at  331/ 

88  yd.  at  331/ 

92  yd.  at  121-/ 

48  yd.  at  121/ 

96  yd.  at  371/ 

65  yd.  atl6f/ 

84  yd.  at  121/ 

:051yd.  at  10/ 

37  yd.  at  101/ 

165  yd.  at  25/ 

232  yd.  at  11/ 

42  yd.  atSL25 

192  yd.  at  121/ 

36  yd.  at  S  1.331 

24  yd.  atS1.66| 

145  yd.  at  5/ 

256  yd.  at  6/ 

178  yd.  at  7/ 

231yd.  at  8/ 

143  yd.  at  9/ 

321yd.  at  11/ 

148  yd.  at  16f/ 

64  yd.  at  S1.25 

24  yd.  atSl.871 

121yd.  at  25/ 

61yd.  at  SI. 331 

36ydoatS1.66f 

1101  yd,  at  10/ 

a. 

16 

h. 

24  yr. 

c. 

64  hr. 

d. 

12  men 

e. 

15  desks 

DENOMINATE   NUMBERS 
CHAPTER  XII 

DENOMINATE  QUANTITIES 
REVIEW  OF   THE   COMMON   TABLES  * 

ORAL  EXERCISE 

1.  Which  of  the  following  numbers  are  concrete  ?  which  are 
abstract?  which  are  denominate? 

/.  150  k.    36  min. 

^.  21  yd.  L    5  yd.  2  ft. 

h.  65  A.  m.    3  yr.  4  mo. 

i.  17  books  n.    10  T.  75  lb. 

y.  34  houses  o.,  5  A.  61  sq.  rd. 

2.  Define  an  abstract  number;  a  concrete  number;  a  de- 
nominate number;  a  simple  number ;  a  compound  number. 

3.  Which  of  the  numbers  in  question  1  are  simple  ?  which 
are  compound  ? 

ORAL  EXERCISE 

1.  Repeat  the  table  of  avoirdupois  weight. 

2.  Repeat  the  table  of  long  measure;  of  surveyors'  long 
measure;  of  square  measure  ;  of  surveyors'  square  measure. 

3.  Repeat  the  table  of  cubic  measure;  of  dry  measure;  of 
liquid  measure;  of  time  ;  of  angular  measure;  of  United  States 
money  ;  of  English  money. 

4.  Name  a  number  expressing  distance ;  two  numbers  ex- 
pressing area  ;  two  expressing  value  ;  three  expressing  capacity. 

5.  How  many  statute  miles  in  a  degree  of  the  earth's  sur- 
face at  the  equator  ?  how  many  geographical  miles  ?  How 
many  feet  in  a  statute  mile  ?  how  many  inches  ? 

1  Tables  of  weights  and  measures  may  be  found  in  the  Appendix  B. 


170  COKCISE   BUSINESS   ARITHMETIC 

EEDUCTION 

ORAL  EXERCISE 

1.  Change  42  ft.  to  inches ;  to  yards. 

2.  Express  15  yd.  as  feet ;  as  inches. 

3.  Reduce  80  qt.  to  gallons ;  to  pints. 

4.  Change  128  qt.  to  pecks ;  to  bushels. 

5.  Express  120  pt.  as  quarts ;  as  gallons. 

6.  What  part  of  a  yard  is  2  ft.?  J  ft.?  {  ft.? 

7.  Reduce  5  bu.  to  pecks ;  to  quarts  ;  to  pints. 

Reduction  Descending 
174.    Example.     Reduce  4  T.  75  lb.  to  ounces. 

Solution.  Since  1  T.  =  2000  lb.,  4  T.  =  4  times  2000 
2000  lb.  =  8000  lb.;  and  with  the   75  lb.   added  this  =  4 

8075  lb.  Since  1  lb.  =  16 oz.,  8075  lb.  =  8075  times  16  oz.  oQ-rr 
=  129,200  oz.,  the  required  result.  ^  n 

8075  times  16  oz.  =  16  times  8075  oz.;  therefore  8075  — 

times  16  oz.  is  found  as  shown  in  the  margin.  129^00,  No,  01  OZ. 

WRITTEN  EXERCISE 

Reduce : 

1.  115'  6''  to  inches.  5.  3|  rd.  to  feet. 

2.  12  bu.  4  qt.  to  pecks.  6.  IJ  T.  to  ounces. 

3.  «£  16  158.  to  shillings.  7.  12  A.  to  square  feet. 

4.  211  rd.  3  ft.  to  inches.  8.  161  cd.  to  cubic  feet. 

ORAL  EXERCISE 

1.  How  many  pecks  in  \  bu.?  in  |  bu.? 

2.  Change  .25  A.  to  square  rods;  .375  A.;  75  A. 

3.  Reduce  J  gal.  to  pints.     Express  ^  rd.  as  inches;  as  yards. 

WRITTEN  EXERCISE 
Reduce: 

1.  I  mi.  to  feet.  4.    ^  yd.  to  inches. 

2.  .75  cd.  to  cubic  feet.  5.    .375  mi.  to  feet. 

3.  -Ill  A.  to  square  feet.  6.    -^^  hr.  to  seconds. 


DENOMINATE   QUANTITIES  171 

Reduction  Ascending 

175.  Example.  Express  176  qt.  dry  measure  in  higher  de- 
nominations. ^_^       o       r»r.  ^^1 

176 -f- 8  =  22,  or  22  pk. 

Solution.    Since  8  qt.  =  1  pk.,  divide  by  8        90_t,4._c;        /i 
and  obtain  as  a  result  22  pk.  Since4pk.  =  lbu.,  *   ^  ~  *^  ^^^  ^  ^®" 

divide  by  4  and  obtain  as  a  result  5  bu.  2  pk.  mamder  01  2, 

or  5  bu.  2  pk. 

WRITTEN  EXERCISE 

Reduce  to  higher  denominationB : 

1.  3840  ft.                   5.    816  pk.  9.  15,120". 

2.  1054  pt.                   6.    106,590  ft.  10.  51,200  cu.  ft. 

3.  14,400  sec.               7.   43,560  sq.  in.  li.  145,152  cu.  in. 

4.  2000  sq.  in.             8.   27,900  lb.  avoir.  12.  27,900  oz.  avoir. 

ORAL  EXERCISE 

1.  Reduce  ^  ft.  to  the  fraction  of  a  yard. 

2.  Change  .16  cwt.  to  the  decimal  of  a  ton. 

3.  What  part  of  a  yard  is  1  in.?  2  in.?  J  in.? 

4.  What  decimal  part  of  an  acre  is  16  rd.?  40  rd.? 

5.  What  part  of  35  bu.  is  7  bu.?  of  IJ  bu.  is  J  bu.? 

WRITTEN   EXERCISE 

1.  Reduce  1|  in.  to  the  fraction  of  a  foot ;  of  a  yard. 

2.  Reduce  10«.  ^d.  to  the  fraction  of  a  pound  sterling. 

Solution.     There  are  12d.  in  a  shilling  and  20s.  10s.and9(^.  =  129c?. 

in  a  pound  sterling,  or  240d!.  a-j 940^ 

To  find  what  fractional  part  of  a  pound  sterling  cq't-* 

10s.  and  9d.  are,  use  the  following  statement :  2^^  0"  ~  '*^oiO^ 

10s.  M.  =  \2M.  £\  =  240d.  Therefore,  10s.  9d.=  Or  ^£.5375 
m  of  a  £,  or  £.5375. 

3.  Reduce  4  yd.  IJ  ft.  to  the  decimal  of  a  rod. 

4.  Reduce  10s.  Gc?.  2  far.  to  the  decimal  of  a  pound  sterling. 

5.  Reduce  5  T.  721  lb.  to  tons  and  decimal  of  a  ton;  6  T. 
1750  lb.;  12  T.  290  lb.;  29,240  lb.;  28,390  lb. 

6.  Find  the  cost  of  1750  lb.  of  coal  at  $6.25  per  ton;  of 
2170  lb.;  of  690  lb.;  of  1360  lb.;  of  3240  lb.;  of  32590  lb. 


172 


CONCISE   BUSINESS  ARITHMETIC 


ADDITION  AND    SUBTRACTION 


ORAL 

EXERCISE 

State  the  sum 

Of: 

1. 

2. 

3. 

4. 

12  ft.  1  in. 

5  lb.  8  oz. 

15  rd.  5  ft. 

10  mi.  8  rd. 

6       3 

6       3 

17        2 

8 

40 

State  the  difference  between : 

5. 

6. 

7. 

8. 

90  mi.  300  rd. 

75  rd.  121 J 

ft. 

30  yd.  2  ft. 

44  bu.  3  pk. 

75        120 

26          41 

— 

17    n 

29 

1 

WRITTEN   EXERCISE 

Find  the  sum 

of: 

1. 

2. 

3. 

4. 

£140  6s. 

£139  5s. 

84  T.  75  lb. 

279  T 

.  840  lb. 

159  3 

214  5 

96 

14 

364 

210 

162  4 

921  3 

78 

79 

872 

220 

139  2 

141  7 

37 

41 

146 

140 

167  4 

10  9 

19 

63 

214 

180 

129  3 

171  8 

84 

79 

926 

230 

136  4 

215  7 

97 

13 

210 

420 

147  2 

321  5 

87 

125 

75 

750 

Find  the  difference  between : 

5. 

6. 

7. 

8. 

11  mo.  17  da. 

11  mo.  1  da. 

8  mo.  14  da. 

9  mo.  17  da. 

8         31 

9       31 

2         29 

2 

31 

9.  An  English  merchant  had  on  hand  Jan.  1  goods  valued 
at  £5927  10s.;  during  the  following  six  months  he  bought 
goods  at  a  cost  of  £4920  10s.  and  sold  goods  to  the  amount 
of  £7926  4s.  If  the  value  of  the  goods  on  hand  July  1  of  the 
same  year  was  £4120  10s.,  what  was  the  gain  or  the  loss  in 
English  money  ?    in  United  States  money  ? 


DENOMINATE  QUANTITIES  173 

MULTIPLICATION   AND  DIVISION 

ORAL  EXERCISE 

Multiply:  Divide: 

1.  3  ft.  by  6.  7.   27  yd.  by  9. 

2.  IJ  mi.  by  8.  8.   225  ft.  by  71  ft. 

3.  9  lb.  4  oz.  by  2.  9.   48  ft.  6  in.  by  2. 

4.  18  lb.  1  oz.  by  9.  10.   540  yd.  by  18  yd. 

5.  17  yd.  2  in.  by  9.  11.   164  lb.  12  oz  by  4. 

6.  19  gal.  1  qt.  by  3.  12.    640  mi.  160  rd.  by  20. 
176.    Examples,     l.   How  much  hay  in  8  stacks  each  contain- 
ing 5  T.  760  lb.  ? 

Solution.     8  times  760  lb.  =  6080  lb.  =  3  T.  80  lb. ;         5  x.  760  lb. 
■write  80  in  place  of  pounds  and  carry  3.     8  times  5  T.  =  ^ 

40  T. ;  40  T.  +  3  T.  carried  =  43  T.    The  required  result 


is  therefore  43  T.  80  lb.  43  T.      80  lb. 

2.  An   importer   paid  <£  87  10s.  for   50  pc.  of  bric-a-brac. 

What  was  the  cost  per  piece  ? 

Solution.     Since  50  pc.  cost  £87  10s.,  1  pc.  costs  £     1      15s. 

3^  of  £  87  10s.     ^V  of  £  87  =  £  1  with  an  undivided  re-      ^0\£  ^7 IQ^ 

mainder  of  £  37  ;   write  £  1  in  the  quotient  and  add  -^ 

£  37  to  the  next  lower  denomination ;  £  37  10s.  =  750s.     -^-^  of  750s.  =  15s. 

3.  At  10 s.  Qid.  per  yard,  how  many  yards  can  be  bought  for 
X  15  15s.  ? 

Solution.     The  dividend  and 
divisor   are     concrete    numbers; 

therefore     reduce    them    to    the  <£  15  15s.  =  3780a. 

same  denomination  before  divid-  lOs.  6c?.       =  126c?. 

ing.    £15  15s.  =  2,imd.,  10s.  6d        3739^  ^  i^Qd.  =  30,  no.  of  yd. 

=  VIM.      3780(?.  -  126c?.  =  30 ; 
that  is  30  yd.  can  be  bought. 

ORAL  EXERCISE 

1.  At  72  ^  per  gross  what  will  2  doz.  buttons  cost  ?  4  doz.  ? 
7  doz.  ? 

2.  How  many  3-oz.  packages  can  be  put  up  from  4  lb.  of 
pepper  ? 

3.  Find  the  cost  of  3  T.  of  bran  at  30^  per  hundredweight; 
of  5  T.  at  50  ^  per  hundredweight. 


174  CONCISE   BUSINESS   ARITHMETIC 

4.  How  many  1-lb.  packages  can  be  put  up  from  15  T.  of 
breakfast  food  ? 

5.  When  coal  is  $  6  per  ton  what  will  7000  lb.  cost  ?  6400 
lb.?  3600  lb.? 

6.  Find  the  cost  of  2400  lb.  of  flour  at  $  2.25  per  hundred- 
weight; of  4400  lb.;  of  3200  lb. 

7.  At  12 J  ^  per  quire  what  will  480  sheets  of  paper  cost  ? 
240  sheets  ?  2880  sheets  ?  720  sheets  ? 

8.  I  buy  3  qt.  of  milk  per  day.  If  I  pay  8  f^  per  quart, 
what  is  my  bill  for  July  and  August  ? 

9.  I  bought  3  gro.  pens  at  60  ^  a  gross  and  sold  them  at  the 
rate  of  2  for  1  ^  ;  what  was  my  gain  or  loss  ? 

10.  I  bought  3|-  bu.  of  apples  at  f  1.00  per  bu.  and   sold 
them  at  50  ^  a  peck.     What  was  my  gain  ? 

11.  I  sold  4 J  cd.  of  wood  for  $27  and  thereby  lost  $9  on 
the  cost.     What  was  the  cost  per  cord  ? 

WRITTEN  EXERCISE 

1.  Find  the  cost  of  10  pwt.  7  gr.  of  old  gold  at  $1.25  per 
pennyweight;  of  12  pwt.  4  gr.  at  f  1.10  per  pennyweight. 

2.  I  bought  3 J  A.  of  city  land  at  $125  an  acre  and  sold  it 
at  50  ^  per  square  foot.     Did  I  gain  or  lose  and  how  much  ? 

3.  Give  the  length  of  a  double-track  railroad  that  can  be 
laid  with  352,000  rails  30  ft.  long. 

4.  I  bought  a  barrel  of  cranberries  containing  21  bu.  at  $4 
per  bushel  and  retailed  them  at  15^  a  quart.  Did  I  gain  or 
lose  and  how  much  ? 

9.  From  a  farm  of  375  A.  I  sold  25|  A.  What  is  the  re- 
mainder worth  at  $125  per  acre  ? 


PERCENTAGE   AND   ITS   APPLICATIONS 
CHAPTER   XIII 

PERCENTAGE 
ORAL  EXERCISE 

1.  .50  may  be  read  fifty  hundredths^  one  half  or  fifty  per 
cent.     Read  each  of  the  following  in  three  ways  ;  .  25, .  30, 12 J  % . 

2.  Read  each  of  the  following  in  three  ways  :  •^,  J,  ^,  J,  gV' 
h  h  h  h  h  2  %  21%,  125%,  6J%,  81%,  66|%,  250%,  375%. 

3.  50  %  of  a  number  is  .50  or  ^  of  the  number.     What  is 
50%  of  $600?    25%?    121-%?    io%?    40%?    20%?    75%? 

177.  Per  cent  is  a  common  name  for  hundredths. 

178.  The  symbol  %  may  be  read  hundredths  ov  per  cent. 

179.  Percentage  is  the  process  of  computing  by  hundredths 
or  per  cents. 

ORAL  EXERCISE 
Express  as  per  cents : 

1.  .28.         3.    .001  5.    .331.  7.    .621  9.    .5. 

2.  .37.        4.    .142.  6.    .28f         8.    .0075.      10.    .2. 
Express  as  decimal  fractions  : 

11.  20%.    13.    72%.        15.    1%.         17.    125%.     19.    ^%. 

12.  45%.    14.    18%.       16.    \%.        18.    250%.     20.    375%. 
Express  as  common  fractions  : 

21.  1%.       23.     21%.  25.     1331%.    27.     871%.       29.     1%. 

22.  2%.       24.     3i%.         26.    266|%.   28.    1121%.    30.    175%. 
Express  as  per  cents  : 

31.  \.  33.    Jj.  35.     1\.  37.    f.  39.    f. 

32.  1  34.    ^^.  36.    2f.  38.    IJ.  40.    •^. 

175 


176 


CONCISE   BUSINESS   AEITHMETIC 


Important  Per  Cents  and  their  Fractional  Equivalents 


Pee 

Cent 

Fractional 

Value 

Per 

Cent 

Fractional 
Value 

Pee 

Cent 

Fractional 
Value 

Per 

Cent 

Fractional 
Value 

121% 

25% 

371% 

50% 

621% 

1 
I 

f 

1. 

i 

75% 

100% 

16f% 

33|% 

06f% 

831% 
20  % 
40% 
G0% 
80% 

f 
1 

1 

6i% 

6f% 

81% 

111% 

14r/o 

i 

180.  The  terms  used  in  percentage  are  the  base,  the  rate, 
and  the  percentage.  The  base  is  the  number  of  which  a  per 
cent  is  taken  ;  the  rate,  the  number  of  hundredths  of  the  base 
to  be  taken ;  the  percentage,  the  result  obtained  by  taking  a 
certain  per  cent  of  the  base. 

In  the  expression  *'  12%  of  1 50  is  $  6,"  $  50  is  the  base,  12  %,  the  rate,  and 
$  6,  the  percentage. 

181.  The  base  plus  the  percentage  is  sometimes  called  the 
amount ;  the  base  minus  the  percentage,  the  difference. 


FINDING  THE   PERCENTAGE 

182.    Example.     What  is  15  %  of  $  660  ? 

Solution.     15%  of  a  number  equals  .15  of  it.     .15  of  ^660  = 
$  99,  the  required  result. 


$660 
.15 


$99.00 

183.    Obviously,  the  product  of  the  base  and  rate  equals  the 
percentage. 

The  base  may  be  either  concrete  or  abstract.     The  rate  is  always  abstract. 
The  percentage  is  always  of  the  same  name  as  the  base. 

ORAL  EXERCISE 

1.  What  aliquot  part  of  1  is  .121  ?    .25  ?   -.50  ?    .16|  ?   .331  ? 
.20?  .06J?  .06f?  .081?  .111?  .142?  371%?  621  %?  66f  %  ? 

2.  Formulate  a  short  method  for  finding  12|^  %  of  a  number. 
Solution.     12|  %  =  .12|  =  \  ;  hence,  to  find  12|  %  of  a  number,  divide  by  8. 

3.  State   a  short   method   for   finding   25%  of   a  number; 
50%;    16|%;    33^%;    20%;    6^  % ;    6|%  ;    8J  % ;    111%. 


PERCENTAGE  177 

To  guard  against  absurd  answers  in  exercises  of  this  character  estimate 
the  results  in  advance  as  explained  on  pages  44  and  128. 

4.  Find   50%    of  960.     Also   25%;  371%;  121%;  62i%; 
75%;  16f%;   331%;  66|%;   831%;  20%;  40%;   60%;   6i%. 

5.  By  inspection  find  : 

a,  50%  of  1792.  e,  25%  of  8 1729.  ^.    66f  %  of  2460. 

h.  371%  of  $320.  /.  6f%  of  16600.  j.    331%  of  2793. 

c.  121%  of  1880.  g,  61%  of  3296.  h.    81%  of  24,960. 

d,  16f  %  of  $669.  h.  831%  of  4560.  I.   20%  of  12,535. 

ORAL    EXERCISE 

1.  Find  10%  of  720;    of  $15.50;    of  120  men;   of  $127.50. 

2.  What  aliquot  part  of  10%  is  5%  ?  21  %  ?  11%  ?  31%  ?  If  %  ? 

3.  Formulate  a  short  method  for  finding  1 J  %  of  a  number. 

Solution.     1^%  of  a  number  is  |  of  10%  of  the  number  ;  hence,  to  find  \\% 
of  a  number,  point  off  one  place  to  the  left  and  divide  by  8. 

4.  State  a  short  method  for  finding  5  %  of  a  number ;  2 J  %  ; 
3l%;lf%. 

5.  By  inspection  find  : 

a.   5%  of  720.  d,   1|%  of  1840.         g.   31%  of  $3900. 

h.   21%  of  840.  e.   If  %  of  $366.         h.  1|  %  of  120  mi. 

c.   31%  of  1560.         /.   21%  of  $720.         L   1\%  of  1632  A. 

ORAL  EXERCISE 

1.  Compare  24%  of  $25  with  25%,  of  $24;    24%  of  $2500 
with  25  %  of  $2400.     What  is  32  %  of  $25  ? 

Solution.    32  %  of  §  25  =  25  %  of  $  32  =  ^  of  $  32  =  $  8,  the  required  result. 

2.  What  is  125%  of  $880? 

Solution.    125%  =  1.25  =  |  of  10;   \  of  $8800  (10  times  $880)  =$1100. 

3.  Find  125%   of  400;  of  640;  of  3200;  of  160 ;  of  1280. 

4.  Formulate  a  short  method  for  finding  166f  %  of  a  num- 
ber ;  333 J  %  of  a  number ;  250  %  of  a  number. 

5.  Compare  88  %  of  12,500  bu.  with  125  %  of  8800  bu. 

6.  Find  32%  of  $125;  of  $1250;  of  $12,500;  of  $125,000. 

7.  Find  250%  of  $720;  of  $3200;  of  $28,800;  of  864,800, 


178  CONCISE   BUSINESS   ARITHMETIC 

ORAL  EXERCISE 

By  inspection  find  : 

1.  48  %  of  250.  5.  180  %  of  625. 

2.  32%  of  125.  .  ,             6.  160%  of  875. 

3.  128%  of  250.  7.  240%  of  7500. 

4.  16%  of  2500.  8.  125%  of  $240.40. 

WRITTEN  EXERCISE 

1.  A  farmer  sold  640  bu.  wheat,  receiving  $1.05  per  bushel 
for  87 J  %  of  it  and  85^  per  bushel  for  the  remainder.  What 
was  the  total  amount  received  ? 

2.  A  grocer  compromised  with  his  creditors,  paying  60  %  of 
the  amount  of  his  debts.  If  he  owed  A  f  756,  B  $1250,  and  C 
$3750,  how  much  did  each  receive  ? 

3.  A  merchant  sold  360  bbl.  apples  for  $1200.  If  he  re- 
ceived $3.50  per  barrel  for  66|%  of  the  apples,  what  was  the 
price  received  per  barrel  for  the  remainder  ? 

4.  A  man  bought  a  house  for  $12,864.75;  he  expended  for 
improvements  33J  %  of  the  first  cost  of  the  property,  and  then 
sold  it  for  $20,000.     Did  he  gain  or  lose,  and  how  much  ? 

5.  A  commission  merchant  bought  1200  bbl.  apples  and 
after  holding  them  for  3  mo.  found  that  his  loss  from  decay 
was  10%.  If  he  sold  the  remainder  at  $3.75  per  barrel,  how 
much  did  he  receive  ? 

6.  A  merchant  prepaid  the  following  bills  and  received  the 
per  cents  of  discount  named:  4%  on  bill  of  $875.50;  6%  on 
bill  of  $378.45;  2%  on  bill  of  $940.50;  3J%  on  bill  of  $400. 
What  was  the  net  amount  paid  ? 

FINDING   THE   RATE 

ORAL  EXERCISE 

1.  8  is  what  part  of  40  ?  what  per  cent  of  40  ? 

2.  90  is  what  per  cent  of  270  ?  of  360  ?  of  450  ? 

3.  70  is  what  per  cent  of  560?  of  630  ?  of  700  ? 

4.  The  base  is  900  and  the  percentage  450 ;  what  is  the  rate  ? 


PERCENTAGE  179 


184.   Example.    135.50  is  what  per  cent  of  f  284? 
Solutions,     a.   ^35.50  is  ^W^^^  or  |  of  {a) 


$284.     $284   is  100%  of   itself;    hence,  '    -AAMr  =  i  =  121^ 


$35.50,  which  is  \  of  $284,  must  be  |  of 

100%,  or  12^<%.     Or,  C^) 

6.    Since  the  product  of  the  base  and  __J^5  =  12J  % 

the  rate   is  the  percentage,  the   quotient  284)35.50 

obtained  by  dividing  the  percentage  by  the  base  is  the  rate. 

185.    Obviously,  thQ  'percentage  divided  hy  the  base  equaU  the 
rate, 

ORAL  EXERCISE 


What  per  cent  of: 

1.    95  is  19? 

7. 

1.6  is  .008? 

2.   4.8  is  1.2? 

8. 

1  yd.  is  1  ft.  ? 

3.  $35is$17i? 

9. 

2  da.  are  8  hr.  ? 

4.    225  A.  are  75  A. 

? 

10. 

4T.  are  3000  lb.? 

5.    34  bu.  are  34  bu. 

? 

11. 

1  yr.  are  4  mo.  ? 

6.   34  bu.  are  68  bu. 

? 

12. 

2  mi.  are  80  rd.? 

WRITTEN  EXERCISE 

1.  A  man  bought  a  house  for  17500  and  sold  it  for  $8700. 
What  per  cent  did.  he  gain  ? 

2.  In  a  certain  city,  school  was  in  session  190  da.  A  lost  38 
da.     What  per  cent  of  the  school  year  did  he  attend? 

3.  An  agent  sold  a  piece  of  property  for  $8462.50  and  re- 
ceived $338.50  for  his  services.  What  per  cent  did  he 
receive  ? 

4.  A  commission  agent  sold  28,600  bu.  of  grain  at  50^  per 
bushel  and  received  for  his  services  $357.50.  What  per  cent 
did  he  receive  on  the  sales  made  ? 

5.  Smith  and  Brown  engaged  in  business,  investing  $18,000. 
Smith  invested  $10,440,  and  Brown  the  remainder.  What  per 
cent  of  the  total  capital  did  each  invest  ? 

6.  An  agent  for  a  wholesale  house  earned  $165.55  during 
the  month  of  May.  If  the  goods  sold  amounted  to  $  1505,  what 
per  cent  did  he  receive  on  the  sales  made  ? 


180  CONCISE   BUSINESS   AKITHMETIC 

FINDING   THE   BASE 
ORAL  EXERCISE 

1.  What  is  5%  of  240  bu.  ? 

2.  12  bu.  is  5  %  of  how  many  bushels  ? 

3.  160  is8%  of  whatnuraber?  4%?  2%  ?  1%  ?  |%  ?  1%  ? 

4.  The  multiplicand  is  400  and  the  multiplier  10;  what  is 
the  product?  The  product  is  2000  and  the  multiplicand  100; 
what  is  the  multiplier  ?  The  product  is  4000  and  the  multi- 
plier 20  ;    what  is  the  multiplicand  ? 

5.  In  percentage  what  name  is  given  to  the  product  ?  to 
the  multiplicand?  to  the  multiplier?  When  the  base  and  rate 
are  given,  how  is  the  percentage  found  ?  When  the  percentage 
and  base  are  given,  how  is  the  rate  found  ?  When  the  per- 
centage and  rate  are  given,  how  is  the  base  found  ? 

186.  Example.    37.5  is  25%  of  what  number? 

Solution.     25%  or  I  of  the  number  =  37.5 
.  •.  the  number  =  37.5  -^  ^  =  150. 

187.  Obviously,  the  quotient  of  the  percentage  divided  hy  the 
rate  equals  the  base. 

WRITTEN  EXERCISE 

1.  N  invested  30%  of  the  capital  of  a  firm,  H  35%,  and  W 
the  remainder,  $1400.     What  was  the  capital  of  the  firm? 

2.  During  the  month  of  May  the  sales  of  a  clothing  mer- 
chant amounted  to  $4864.24,  which  was  8%  of  the  total  sales 
for  the  year.    What  were  the  total  sales  for  the  year? 

3.  B  sold  his  city  property  and  took  a  mortgage  for  $4375, 
which  was  17|%  of  the  value  of  the  property.  If  the  balance 
was  paid  in  cash,  what  was  the  amount  of  cash  received? 

4.  In  compromising  with  his  creditors,  a  man  finds  that  his 
assets  are  $270,900,  and  that  this  sum  is  43%  of  his  entire  in- 
debtedness.     What  will  be  the  aggregate  loss  to  his  creditors? 

5.  The  aggregate  attendance  in  the  schools  of  a  certain  city 
for  1  da.  was  43,225  students.  If  this  number  was  95%  of  the 
number  of  students  belonging,  how  many  students  were  absent? 


PERCEKTAGE  181 

PER  CENTS  OF  INCREASE 

ORAL  EXERCISE 

1.  If  2|  times  a  number  is  50,  what  is  the  number? 

2.  If  2.5  times  a  number  is  75,  what  is  the  number? 

3.  If  250%  of  a  number  is  $1250,  what  is  the  number? 

4.  If  250%  of  a  number  is  150,  what  is  the  number?     If 
250*%  is  125,  what  is  the  number? 

5.  If  300%  of  a  number  is  $5400,  what  is  the  number? 

188.    Examples,     l.    A   man   sold    a   farm    for    $3900    and 
thereby  gained  30%.     How  much  did  the  farm  cost? 

Solution.     1.30  of  the  cost  =  $  3900. 

.  •.  the  cost  =  $3900  -f- 1.30  =  $  3000. 

2.    What  number  increased  by  33  J  %  of  itself  equals  180? 

Solution,     f  of  the  number  =  180 

.  •.  the  number  =  180  s-  f  =  135. 


G|%  of  itself  is  480? 
125%  of  itself  is  900? 
371%  of  itself  is  440? 
11-1%  of  itself  is  300? 
14f%  of  itself  is  328? 
200%  of  itself  is  2700? 
300%  of  itself  is  2800? 

WRITTEN  EXERCISE 

1.  I  sold  375  bu.  of  wheat  for  $427.50,  thereby  gaining  20%. 
How  much  did  the  wheat  cost  me  per  bushel? 

2.  A  fruit  dealer  sold  a  quantity  of  oranges  for  $6.75.     If 
his  gain  was  12^%,  what  did  the  oranges  cost  him? 


ORAL  EXERCISE 

What  number  increased  hy: 

1. 

10% 

of  itself  is 

220? 

8. 

2. 

25% 

of  itself  is 

125? 

9. 

3. 

50% 

of  itself  is 

300? 

10. 

4. 

75% 

of  itself  is 

700? 

11. 

5. 

6i% 

of  itself  is 

170? 

12. 

6. 

12^^ 

9  of  itself  i 

s  180? 

13. 

7. 

66i^ 

'0  of  itself  is  135? 

14. 

3.  My  savings  for  March  increased  331%  over  February.  If 
my  savings  for  March  were  $84.36,  what  were  my  savings  for 
February  and  March? 


182  COKCISE   BUSINESS   AKITHMETIC 

PER  CENTS   OF  DECREASE 

ORAL  EXERCISE 

1.  "What  per  cent  of  a  number  is  left  after  taking  away 
33^%  of  it  ?     What  fractional  part? 

2.  If  I  of  a  number  is  600,  what  is  the  number  ?  If  66|  %  of 
a  number  is  75,  what  is  the  number  ? 

3.  A  man  spent  40%  of  his  money  and  had  |60  remaining. 
How  much  had  he  at  first  ?    How  much  did  he  spend? 

189.  Examples,  l.  A  man  sold  a  horse  for  $332,  thereby 
losing  IT  %,     What  was  the  cost  ? 

Solution.     0.83  of  the  cost =$332. 

.  •.  the  cost  =  $  332  --  0. 83  =  $  400. 

2.    What  number  decreased  by  25  %  of  itself  equals  $375? 

Solution.     |  of  the  number  =  $  375. 

.  •.  the  number  =  $  375  ^  |  =  $  500. 

ORAL  EXERCISE 

What  number  diminished  by: 

1.  ^  %  of  itself  equals  75  ?  4.  -J  of  itself  equals  750  ? 

2.  81%  of  itself  equals  440?  5.  J%  of  itself  equals  99.5? 

3.  6f  %  of  itself  equals  280?  6.  1%  of  itself  equals  49.5? 

WRITTEN  EXERCISE 

1.  Of  what  number  is  9581.88   77  %  ? 

2.  A  merchant  sold  1200  bu.  of  potatoes  for  $640,  which 
was  16|^  %  less  than  he  paid  for  them.  What  was  the  cost  per 
bushel? 

3.  In  selling  a  carriage  for  $75  a  merchant  lost  25%  on  the 
cost.  What  was  the  asking  price  if  the  carriage  was  marked 
to  gain  25  %  ? 

4.  A  newsboy  sold  92  papers  on  Tuesday.  If  this  number 
was  23  J  %  less  than  the  number  sold  on  Monday,  how  many 
papers  were  sold  on  the  two  days  ? 

5.  A  dealer  sold  a  quantity  of  apples  at  1 6  per  barrel,  and 
by  so  doing  lost  16f  %.  If  he  paid  $309.60  for  the  apples, 
how  many  barrels  did  he  buy  ? 


PEECENTAGE 


183 


ORAL  REVIEW  EXERCISE 

1.  By  inspection  find  12|  %  of  the  following  numbers  : 

a.  1872.               e.  12464.  i.  $1688.              m.  124.72. 

h.  648  bu.          /.  2696  A.  j.  2072  A.            n.   $168.48. 

t?.   1264  A.          ^.  1624  ft.  A:.  11,464  mi.        o.    $176.24. 

d.  960  mi.           h,  1832  mi.  I.   37,128  mi.       p.  $2184.32. 

2.  By  inspection  find  10  %  of  each  of  the  above  numbers ; 
25%;  125%;  20%. 

3.  State  the  missing  term  in  each  of  the  following : 


No. 

Base 

Kate 

Pkbckntagk 

No. 

Babe 

Bate 

Percentage 

a. 

$600 

n% 

? 

/• 

966 

16f% 

? 

b. 

$650 

? 

$39 

ff- 

? 

8i% 

15  bu. 

c. 

? 

4% 

$18 

h. 

1275 

61% 

? 

d. 

900 

? 

720 

i. 

? 

6i% 

21  mi. 

e. 

? 

4% 

20 

J- 

400 

? 

600 

4.  By  inspection  find  10  %  of  each  of  the  following  : 

a,  $264.  d.  $840.  g.  $232.  j,  $2448. 

5.   $920.  e,   $750.  A.  $144.  k.  $1432. 

(?.   $720.  /.   $364.  ^.  $288.  ?.   $3624. 

5.  By  inspection  find  1^  %  of  each  of  the  above  numbersj 


lf%;   1000%;   125%;   166f% 


WRITTEN  REVIEW  EXERCISE 

1.    A  collector  charged  4  %  on  all  amounts  collected. 


If  he 

remitted  to  his  customers  in  one  month  $3720.48,  how  much 
did  he  receive  for  his  services? 

2.  A  father  left  to  his  son  60  %  of  his  estate  and  to  his 
daughter  the  remainder,  $9390.88.  What  was  the  value  of  the 
estate  and  how  much  did  the  son  receive  ? 

3.  A  farmer  planted  1  bu.  3  pk.  of  oats  on  an  acre  of  ground 
and  harvested  bQ  bu.  What  per  cent  of  the  yield  was  the 
planting?     What  per  cent  of  the  planting  was  the  yield? 

4.  A  merchant  paid  the  following  charges  on  a  bill  of  goods : 
cartage  $12.45,  freight  $65.32,  insurance  $41.  If  the  charges 
represent  5  %  of  the  face  of  the  bill,  what  was  the  gross  cost  of 
the  goods? 


184  CONCISE   BUSINESS   ARITHMETIC 

5.  A  man  had  6  A.  of  land;  to  one  party  he  sold  a  piece 
25  rd.  by  20  rd.,  and  to  another  party  140  sq.  rd.  What  per 
cent  of  the  field  remained  unsold? 

6.  In  a  recent  year  191,571,750  lb.  of  fish  were  landed  in 
Boston  and  Gloucester,  and  of  this  quantity  103,460,410  lb. 
were  landed  m  Gloucester  and  88,111,340  in  Boston.  What 
per  cent  of  the  total  was  furnished  by  each  city?  (Correct 
to  the  nearest  .01.) 

7.  A  owned  property  valued  at  $12,000  from  which  he 
received  a  yearly  rental  of  S  960.  If  he  paid  taxes  amounting 
to  $160,  msurance  $75.50,  and  made  repairs  amounting  to 
$184.50,  what  per  cent  net  income  did  he  receive? 

8.  B  owns  a  field  80  rd.  square.  During  a  certain  year 
this  field  yielded  on  an  average  25  bu.  of  wheat  to  an  acre. 
The  wheat  when  sold  at  $1  a  bushel  produced  an  amount  equal 
to  25  %  of  the  value  of  the  field.  What  was  the  value  of  the 
field? 

9.  A  landowner  rented  a  field  to  a  tenant  and  was  to 
receive  as  rent  16|%  of  the  grain  raised.  The  owner  of  the 
field  sold  his  share  of  the  grain  for  84/  per  bushel,  receiving 
$298.20.  If  the  tenant  sold  his  share  of  the  gram  for  the  same 
price  per  bushel,  how  much  did  he  receive  ? 

10.  In  a  single  year  the  cost  of  the  cotton  yarn  used  in  the 
manufacture  of  hosiery  and  knit  goods  in  the  state  of  New  York, 
in  round  numbers,  was  $13,825,000;  in  the  state  of  Illinois, 
$1,550,000.  The  cost  of  the  cotton  yarn  used  in  Illinois  was 
what  per  cent  less  than  the  cost  of  the  cotton  yarn  used  in 
New  York,  in  a  year?    (Correct  to  the  nearest  .01.) 

11.  By  a  recent  census  report  it  was  shown  that  the  value 
of  all  personal  property  in  the  state  of  New  York  was 
approximately  $500,000,000  and  the  value  of  all  the  real  estate 
approximately  $10,000,000,000.  Draw  parallel  lines  making 
a  comparison  of  the  personal  property  and  the  real  estate.  The 
real  estate  is  what  per  cent  greater  than  the  personal  property  ? 
The  personal  property  is  what  per  cent  less  than  the  real 
estate  ? 


PERCENTAGE  185 

12.  A  young  man  entered  a  bank  as  cashier  and  at  the  end 
of  the  first  year  his  salary  was  increased  25  %  ;  at  the  end  of 
the  second  year  he  was  given  an  increase  of  20  %  ;  and  at  the 
end  of  the  third  year  he  was  given  an  increase  of  25%,  which 
made  his  salary  $4500.     What  salary  did  he  receive  at  first? 

13.  A  government  statistician  collected  facts  regarding  wages 
and  income  from  nearly  two  thousand  private  manufacturing 
concerns,  and  reported  the  following :  the  average  wages  of  all 
employees,  men,  women,  and  children,  per  year  was  $  263.06,  and 
the  average  net  profit  for  each  employer  was  $  2273.  What  per 
cent  greater  was  the  income  of  each  employer  than  of  each  em- 
ployee?    (Correct  to  the  nearest  .01.) 

14.   The  population  of  three 


Ti  I  I  I  I  I  I  I  I  I  I  1  I  I  I  h  M  I  I  I  I  I  I  I  I  I  H  I 


cities  during  a  certain  year  is 
Aw^^a^^^^^^^a^m^m^^  illustrated  by  the  accompany- 
Bmamma^m^m^^^^^^m  ing  lines,  which  are  drawn  on 

CH^HHHVHHHiHH^H  a  scalc  of  12,500  inhabitants 

to  each  -|-  of  an  inch.  What  is  the  population  of  A,  B,  and  C, 
respectively  ?  The  population  of  each  city  is  what  per  cent  of 
the  population  of  the  three  cities  ? 

15.    The  annual  coal  production  in  the  United  States,  Great 
Britain,  Germany,  and  France 


for  a  certain  year  is  illustrated  h  1 1  1 1  1 1  1 1  1 1 1  1 1 1  li  1 1 1 1 1  1 1 1 1 1 1  itT 


in  the  accompanying  rectan-  United  states 
e^les,  drawn  on  the  scale    of 

°^     '  ^  ^^^      ,  ,      GreatBritain 

50,000,000  short  tons  to  each  —i— 
^  of  an  inch.      During  that  Germajj^ 
year,  how  many  tons    did  the  jYanc© 
United  States,  Great  Britain,  ■■ 

Germany,  and  France,  respectively,  produce  ?  The  produc- 
tion of  each  country  is  what  per  cent  of  the  production  of  the 
four  countries  ?  In  the  same  year  the  rest  of  the  world  pro- 
duced approximately  200,000,000  short  tons.  Illustrate  graph- 
ically the  world's  coal  production  for  that  year.  What  was  the 
world's  approximate  production  this  year? 


186  CONCISE  BUSINESS  AKITHMETIC 

A   REVIEW  EXERCISE 

Illustrate  the  following  problems  by  the  use  of  graphs.  Graph  forms 
are  given  on  pages  126,  133.    Use  the  form  suggested  by  the  instructor. 

1.  Illustrate  graphically  problem  25,  page  88.  Use  the  even 
number  of  thousands  for  each  month. 

2.  In  a  recent  year  the  railway  mileage,  single-track,  of  the 
world  was  as  follows :  America,  325,000  mi. ;  Europe,  200,000  mi. ; 
Asia,  63,000  mi.;  Africa,  23,000  mi.;  Australia,  19,000  mi.  Illus- 
trate graphically,  showing  the  total  mileage,  and  the  relation 
that  each  country  bears  to  the  total. 

3.  In  a  recent  year  there  were  enrolled  in  the  schools  and  col- 
leges of  the  United  States  20,000,000  students,  grouped  accord- 
ing to  ages  as  follows:  5  yr.,  400,000;  6  to  9  yr.,  6,200,000; 
10  to  14  yr.,  9,000,000;  15  to  17  yr.,  3,000,000;  18  to  20  yr., 
1,000,000 ;  21  to  24  yr.,  400,000.  Illustrate  graphically.  Each 
group  is  what  per  cent  of  the  total  ? 

4.  The  number  of  cattle,  other  than  milch  cows,  on  farms  and 
ranches  in  the  United  States,  as  reported  by  the  decennial  cen- 
suses, for  the  years  named  were  as  follows:  1870,  13,500,000; 
1880,  22,500,000 ;  1890,  33,500,000 ;  1900,  50,000,000 ;  1910, 
41,000,000.  Illustrate  graphically.  What  do  these  figures  sug- 
gest regarding  the  cost  of  living  as  applied  to  beef  ? 

5.  The  following  figures  represent  the  latest  estimates  of  the 
wealth  of  the  nations  named.  The  figures  given  represent  bil- 
lions of  dollars:  United  States,  130 ;  Great  Britain  and  Ireland, 
80;  France,  65;  Germany,  60;  Eussia,  40;  Austria-Hungary,  25; 
Italy,  20;  Belgium,  9;  Spain,  5-|-;  Netherlands,  5;  Portugal,  21. 
Switzerland,  2i.     Illustrate  graphically. 

6.  In  a  recent  year  the  cities  of  the  United  States  which 
had  a  population  of  over  100,000  expended  $100,000,000  in 
various  school  expenses,  according  to  the  following  geographical 
divisions:  North  Atlantic  Division,  $54,000,000;  North  Cen- 
tral Division,  $30,000,000;  South  Atlantic  Division,  $2,700,- 
000;  South  Central  Division,  $3,000,000;  Western  Division, 
$10,300,000.     lUustrate  graphically. 


PERCENTAGE  187 

A  WRITTEN  REVIEW  TEST 
(Time,  approximately,  forty  minutes) 

1.  A  gardener  planted  1  qt.  of  corn  and  harvested  5  bu.  What 
per  cent  of  the  planting  was  the  harvest  ? 

2.  A  bookkeeper  made  an  investment  on  which  he  lost  15%. 
If  the  sum  returned  to  him  was  S  1912.50,  what  was  the 
investment  ? 

3.  A  piece  of  cloth,  unfinished,  cost  6/  per  yard.  It  costs 
.75/  per  yard  to  bleach  it,  and  then  it  sells  for  7|/  per  yard. 
The  selling  price  is  what  per  cent  advance  over  the  total  cost  ? 

4.  A  merchant  paid  the  following  bills  less  the  discounts 
named:  $85.50  less  2%;  $141.50  less  3%;  $117.95  less  1%; 
$225.40  less  li%  ;  $47.50  less  2^  %.  What  was  the  total  sum 
paid  ?     What  was  the  total  discount  allowed  ? 

5.  On  Monday  a  man  deposited  in  the  bank  $184.96.  On 
Wednesday  he  deposited  a  sum  121%  greater  than  the  deposit 
of  Monday ;  he  then  drew  a  check  for  50  %  of  his  total  deposit. 
What  was  the  amount  of  the  check  ? 

6.  A  merchant's  sales  increased  the  second  month  of  his 
business  25%  over  the  first  month;  the  third  month  they  in- 
creased 20%  over  the  second  month;  the  fourth  month  they 
decreased  10%  from  the  sales  of  the  third  month.  What  were 
the  sales  for  each  month  if  they  were  $  3240  for  the  fourth  month  ? 

7.  A  farmer  used  1200  lb.  of  potato  fertilizer  per  acre,  on  a 
16-acre  field  of  potatoes.  The  fertilizer  cost  $24,125  per  ton, 
less  5%  for  cash  payment.  If  the  unfertilized  land  produced 
60  bu.  of  potatoes  per  acre,  and  the  fertilized  land  produced 
150  bu.  per  acre,  what  per  cent  of  increase  was  realized  by 
using  the  fertilizer  if  the  potatoes  sold  for  80/  per  bushel? 

8.  A  man  bought  a  piece  of  land,  and  at  the  end  of  the  first 
year  it  had  increased  in  value  25%  ;  at  the  end  of  the  second 
year  it  had  increased  an  additional  8  %  in  value ;  at  the  end  of 
the  third  year  it  had  increased  an  additional  5%  in  value. 
What  did  he  pay  for  the  property  if  at  the  end  of  the  third 
year  it  was  worth  $2551.50? 


CHAPTER  XIV 

COMMERCIAL  DISCOUNTS 
ORAL  EXERCISE 

1.  A  set  of  Scott's  works  is  marked  $12.  If  I  buy  it  at  this 
price,  less  16|%,  what  does  it  cost  me? 

2.  I  buy  890  worth  of  goods  on  30  da.  time,  or  5%  off  for 
cash.     What  cash  payment  will  settle  the  bill  ? 

3.  I  owe  B  8600,  due  in  30  da.  He  offers  to  allow  me  5% 
discount  if  I  pay  cash  to-day.  I  accept  his  offer  and  give  him 
a  check  for  the  amount.     What  was  the  amount  of  the  check  ? 

190.  A  reduction  from  the  catalogue  (list)  price  of  an  article, 
from  the  amount  of  a  bill  of  merchandise,  or  from  the  amount 
of  a  debt,  is  called  a  commercial  or  trade  discount. 

Business  houses  usually  announce  their  terms  upon  their  bill  heads.  The 
space  allowed  for  recording  the  terms  is  usually  limited,  and  bookkeepers 
find  it  necessary  to  use  symbols  and  abbreviations  to  indicate  them.  Thus, 
if  a  bill  is  due  in  30  da.  without  discount,  the  terms  may  be  written 
^/aof  ov  Net  30  da. ;  if  the  bill  is  due  in  30  da.  without  discount,  but  an 
allowance  of  2  %  is  made  for  payment  within  10  da.,  the  terms  may  be 
written  Vio,  ^/so,  or  2  %  10  da.,  net  30  da. 

191.  Manufacturers,  jobbers,  and  wholesale  dealers  usually 
have  printed  price  lists  for  tlieir  goods.  To  obviate  the  neces- 
sity of  issuing  a  new  catalogue  every  time  the  market  changes, 
these  lists  are  frequently  printed  higher  than  the  actual  selling 
price  of  the  goods,  and  made  subject  to  a  trade  discount. 

192.  The  fluctuations  of  the  market  and  the  differences  in 
the  quantities  purchased  by  different  customers  frequently  give 
rise  to  two  or  more  discounts  called  a  discount  series. 

Large  purchasers  sometimes  get  better  prices  and  terms  than  small  pur- 
chasers. Thus,  the  average  customer  might  be  quoted  the  regular  prices 
less  a  trade  discount  of  25  %,  while  an  especially  large  buyer  might  be  quoted 
the  regular  prices  less  trade  discounts  of  25  %  and  10  %. 

188 


COMMERCIAL  DISCOUNTS  189 

193.  When  two  or  more  discounts  are  quoted,  one  denotes  a 
discount  off  the  list  price,  another,  a  discount  off  the  remainder, 
and  so  on. 

The  order  in  which  the  discounts  of  any  series  is  considered  is  not 
material.  Thus,  a  series  of  25  %,  20  %>  and  10  %  is  the  same  as  one  of  20  %, 
10  %,  and  25  %,  or  one  of  10  %,  25  %,  and  20  %. 

194.  Catalogue  prices  are  generally  estimated  on  the  basis  of 
credit  sales,  and  a  cash  purchaser  is  given  the  usual  trade  dis- 
count and  a  special  discount  for  early  payment.  This  latter 
discount  has  the  effect  of  encouraging  prompt  payments. 

The  list  price  is  sometimes  called  the  gross  price  and  the  price  after  the 
discount  has  been  deducted  the  net  price. 

FINDING  THE  NET   PEICE 

195.  Example.  The  list  price  of  a  dozen  pairs  of  shoes  is 
$45.  If  this  price  is  subject  to  a  discount  series  of  20  %  and 
10  %,  what  is  the  net  selling  price  ? 

Solution.    20%  or  ^  of  $45  =  .$9,  the  first  discount. 

$45  —  §9  =  $36,  the  price  after  the  first  discount. 
10%  or  j\  of  $36  =  $3.60,  the  second  discount. 
$36  -  $3.60  =  $32.40,  the  net  selUng  price. 


ORAL  EXERCISE 

Find  the  net  price  : 

List 

Trade 

List        Trade 

List                Trade 

Pkice 

Discount          ] 

Price     Discount 

Price            Discounts 

1. 

$4: 

25%        8. 

$6       40% 

15. 

$4      25%    and  331% 

2. 

$15 

20  %        9. 

$4      121% 

16. 

$30    331%  and  25% 

3. 

190 

331  %     10. 

$24     81% 

17. 

$35    20%    and  25% 

4. 

120 

10  %     <  11. 

$42     16f% 

18. 

$45    20%    andl6f% 

5. 

150 

50%       12. 

$35     20% 

19. 

$50    20%     and  25% 

6. 

12.50  20%       13. 

$100  25% 

20. 

$100  20%     and  10% 

7. 

$^.50  16f  %     14. 

$720  331% 

21. 

$600  161%  and  20% 

22.  A  piano  listed  at  $750  is  sold  less  331  ^,  20  %,  and  10  %. 
What  is  the  net  cost  to  the  purchaser  ? 

23.  A  dealer  offers  cloth  at  $3.50  per  yard  subject  to  a  dis- 
count of  20  %.     How  many  yards  can  be  bought  for  $5Q  ? 


190 


CONCISE   BUSINESS  ARITHMETIC 


WRITTEN    EXERCISE 


Find  the  net  price 


Gross  Gross 

Selling  Price  Trade  Discounts     Selling  Price 

1.  $3360 

2.  $3510 

3.  $4500 


25  %  and  10  % 
331  %  and  20  % 
20  %  and  16f  % 


Trade  Discounts 

4.  $2500    20%,  10%,  and  5% 

5.  $5400    25  %,  20  %,  and  10  % 

6.  $3960     33^%,  20%,andl6f% 

7.  The  list  price  of  cloth  is  $4.80  per  yard,  but  this  price  is 
subject  to  discounts  of  25%  and  20%.  How  many  yards  can 
be  bought  for  $288? 

8.  A  hardware  dealer  sold  25  doz.  5-in.  files  at  $2.50  and 
25  doz.  12-in.  files  at  $7.50,  less  50  %  and  10  %  ;  150  machine 
bolts  at  $21.50  per  C,  less  20  %  and  10  %.  What  was  the  net 
amount  of  the  bill  ? 

9.  Study  the  following  model.  Copy  and  find  the  net 
amount  of  the  bill,  using  the  discounts  named  in  the  bill,  and 
the  following  prices:  5-in. pipe,  $1.45;  1-in.  pipe,  17/;  valves, 
$2.67. 


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Bought  of  GEORGE  W.  MUNSON  &  CO. 


Terms. 


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COMMEKCIAL  BISCOUKTS  191 

10.  One  firm  offers  a  piano  for  §400,  subject  to  discounts  of 
20%  and  20%  ;  another  offers  tlie  same  piano  for  $400  less 
discounts  of  25%  and  15%.  Which  is  the  better  offer?  How 
much  better? 

11.  A  jobber  bought  a  quantity  of  goods  listed  at  $  3600,  sub- 
ject to  discounts  of  25%  and  20  %.  He  sold  the  goods  at  the 
same  list  price,  subject  to  discounts  of  20  %  and  10  %.  Did  he 
gain  or  lose,  and  how  much? 

12.  Make  out  bills  for  the  following,  using  the  current  date 
and  the  name  and  address  of  some  dealer  whom  you  know. 
Terms  in  each  case,  60  da.  net. 

a.  You  bought  12  doz.  hand  saws,  #27,  at  118.50;  7 J  doz. 
mortise  locks,  #271,  at  $4.25;  25  doz.  pocket  knives,  #27,  at 
$7.50;  and  If  doz.  cheese  knives  at  $8.25.    Discount:  25^,10^. 

h.  You  bought  41|^'  of  2"  extra  strong  iron  pipe  at  70^; 
94J'  of  11'^  extra  strong  iron  pipe  at  31J^;  153J'  of  I"  iron 
pipe  at  61^;  88^'  of  ^"  iron  pipe  at  7f  ^.    Discount:  25^,  lO^fc. 

c.  You  bought  25  kitchen  tables  at  $  3. 25 ;  25  dining-room 
tables  at  $8.75;  15  doz.  dining-room  chairs  at  $12.50;  12 
antique  rockers  at  $12.25 ;  and  15  oak  bedroom  sets  at  $32.50. 
Discount:  16|%,  5%. 

FINDING  A  SINGLE  RATE  OF  DISCOUNT  EQUIVALENT 
TO   A   DISCOUNT   SERIES 

196.  Example.  What  single  rate  of  discount  is  equivalent 
to  a  discount  series  of  25  %,  33i  %,  and  10  %  ? 

Solution.    Represent   the    list   price    by  1.00 
100%.    Then,  75%  equals  the  price  after  the  25  (25%  of  100  %) 

first  discount,  50%  the  price  after  the  second  -- 

discount,  and  45  %  equals  the  net  selling  price.  * 

100%,  the  list  price,  minus  45  %,  the  net  selling  _^  (331  %  of  75  %  ) 
price,  equals  55%,  the  single  rate  of  discount  .50 

equivalent  to  the  given  discount  series.  05  TlO  ^   of  50  ^  ^ 

A  single  discount  equivalent  to  a  discount  


series  may  often  be  determined  mentally  (see 


.45 


197, 198).  100  %  -  45  %  =  55  % 


192  CONCISE  BUSINESS  ARITHMETIC 

WRITTEN  EXERCISE 

1.  Find  a  single  rate  of  discount  equivalent  to  a  discount 
series  of  50%,  25%,  20%,  and  10%. 

2.  Which  is  the  better  for  the  buyer  and  how  much,  a  single 
discount  of  65  %  or  a  discount  series  of  25  %,  20  %,  and  20  %  ? 

3.  The  net  amount  of  a  bill  of  goods  was  $  450  and  the  dis- 
counts allowed  were  25%,  33 J%,  and  10%.  Find  the  total 
discount  allowed. 

4.  I  allowed  a  customer  discounts  of  50%,  10  %,  and  10  % 
from  a  list  price.  What  per  cent  better  would  a  single  dis- 
count of  65  %  have  been  ? 

5.  Goods  were  sold  subject  to  trade  discounts  of  25  %,  20  %, 
and  10  %.  If  the  total  discount  allowed  was  $460,  what  was 
the  net  selling  price  of  the  goods  ? 

6.  A  quantity  of  goods  was  sold  subject  to  trade  discounts 
of  20  %  and  20  %.  The  terms  were  60  da.  net  or  5  %  off  for 
payment  within  10  da.  If  a  cash  payment  of  $  1026  was  re- 
quired 3  da.  after  the  date  of  the  bill,  what  was  the  list  price 
of  the  goods  sold  ? 

197.  Since  the  first  of  a  series  of  discounts  is  computed  on 
100  %  of  the  list  price,  and  the  second  on  100  %  minus  the  first 
discount,  it  follows  that  the  sum  of  any  two  separate  discounts 
exceeds  the  equivalent  single  discount  by  the  product  of  the  two 
rates  per  cent. 

Thus,  in  a  discount  series  of  20  %  and  20  %  the  apparent  single  discount  is 
the  sum  of  the  two  separate  discounts  or  40  % ;  but  since  the  second  discount 
is  not  computed  on  100%,  but  on  80%,  40%  exceeds  the  true  single  discount 
by  20  %  of  20  %,  or  4% ;  and  the  equivalent  single  discount  is  40  %  minus  4  %, 
or  36  %.    Hence, 

198.  To  find  the  single  discount  equivalent  to  a  series  of 
two  discounts': 

From  the  sum  of  the  separate  discounts  subtract  their  product^ 
and  the  remainder  will  be  the  equivalent  single  discount. 

When  two  separate  discounts  cannot  be  reduced  to  a  single  discount 
mentally,  proceed  as  in  §196  ;  when  they  can,  proceed  as  in  §198. 


COMMERCIAL  DISCOUNTS  193 

ORAL   EXERCISE 

State  a  single  rate  of  discount  equivalent  to  a  discount  series  of: 

1.  10%  and  10%.  17.  50%  and  5%.  33.  25%  and  8%. 

2.  20%  and  20%.  18.  10%  and  5%.  34.  8^%  and  24%. 

3.  30%  and  30%.  19.  20%  and  5%.  35.  8j%and36%. 

4.  40%  and  40%.  20.  40%  and  5%.  36.  35%andl0%. 

5.  50%  and  50%.  21.  25%  and  30%.  37.  20%andl2|%. 

6.  20%andl0%.  22.  25%  and 40%.  38.  40%andl2i%. 

7.  30%  and  10%.  23.  20%  and  15%.  39.  60%andl2|%. 

8.  40%  and  10%.  24.  40%  and  15%.  40.  12%  and  121%. 

9.  50%  and  10%.  25.  35%  and  20%.  41.  24%andl6f%. 

10.  60%  and  10%.  26.  45%  and  20%.  42.  16|%and20%. 

11.  30%  and  20%.  27.  55%  and  20%.  43.  14f%and35%. 

12.  40%  and  20%.  28.  60%  and  25%.  44.  16|%and25%. 

13.  50%  and  20%.  29.  40%  and  25%.  45.  33J%andl5%. 

14.  60%  and  20%.  30.  60%  and  15%.  46.  66-|%andl5%. 

15.  25%  and  10%.  31.  25%  and  331%.  47.  111%  and  18%. 

16.  35%  and  40%.  32.  45%  and  33^%.  48.  36%  and  111%. 

199.  When  a  discount  series  consists  of  three  separate  rates, 
the  first  two  may  be  combined  as  in  §  198  and  then  the  result 
and  the  third  may  be  combined  in  the  same  manner. 

200.  Example.  Find  a  single  rate  of  discount  equivalent 
to  a  discount  series  of  25%,  20  %,  and  20  %. 

Solution.  — Combine  the  first  two  by  thinking  25%  +  20%-  5%  =  40%,  the 
single  discount  equivalent  to  th^  series  25 %  and  20%.  20%  +  40  %  -8%  =  52%, 
or  the  single  rate  equivalent  to  the  discount  series  25%,  20%,  and  20%. 

ORAL  EXERCISE 
State  a  single  rate  of  discount  equivalent  to  a  discount  series  of: 

1.  20%,  25%,  and  20%.  7.  20%,  10%,  and  10%. 

2.  20%,  15%,  and  10%.  8.  40  %,  10%,  and  10%. 

3.  20%,  20%,  and  20%.  9.  50%,  10%,  and  10%. 

4.  10%,  10%,  and  10%.  10.  30%,  10%,  and  10  %. 

5.  20%,  20%,  and  10%.  11.  20  %,  25%,  and  10%. 

6.  25%,  331%,  and  10%.  12.  20%,  20%,  and  25%. 


194  CONCISE   BUSINESS   ARITHMETIC 

201.  "When  it  is  not  desirable  to  show  the  separate  discounts, 
the  net  selling  price  may  be  found  as  shown  in  the  following 
example. 

202.  Example.  A  mahogany  sideboard  listed  at  $175  is 
sold  subject  to  trade  discounts  of  20%  and  25%.  Find  the 
net  cost  to  the  purchaser. 

Solution.      By  inspectioii  determine  that  a      100  % 40  %  =  GO  % 

discount  of  40%  is  equivalent  to  a  series  of  25%      aC)  cf   of  1^17 'i 11>10'i 

and  20%.    Represent   the    gross   cost   by  100%.  ' 

Then  100%  —  40%  =  60%,  the  net  cost  to  the  purchaser;  that  is,  the  net  cost 
of  the  sideboard  is  60%  of  the  list  price.  60%  of  $175  =  $  105,  the  net  cost  to 
the  purchaser. 

ORAL  EXERCISE 

-By  inspection  find  the  net  cost  of  articles  listed  at: 

1.  $400,  less  20  %  and  25  %.     5.    flOOO,  less  50  %  and  50%. 

2.  1300,  less  20%  and  20%.     6.    $1000,  less  30%  and  10%. 

3.  $600,  less  10  %  and  10  %.     7.    $200,  less  60  %  and  25  %. 

4.  $200,  less  30%  and  30%.     8.    $400,  less  20%  and  40%. 

WRITTEN  EXERCISE 

1.  Find  the  net  selling  price  of  a  piano  listed  at  $450,  less 
20%  and  20%. 

2.  Find  the  net  selling  price  of  an  oak  sideboard  listed  at 
$125,  less  25%,  33^%,  and  10%. 

3.  I  bought  125  cultivators  listed  at  $8.50,  each  subject  to 
trade  discounts  of  20%  and  25%.  If  I  paid  freight  $30.50 
and  drayage  $7.90,  how  much  did  the  cultivators  cost  me? 

4.  The  net  cost  of  an  article  was  increased  $30  by  freight, 
making  the  actual  cost  of  it  $630.  What  was  the  list  price  of 
the  article,  the  rates  of  discount  being  25  %  and  33^  %  ? 

5.  You  desire  to  buy  24,000  ft.  choice  cypress:  one  firm 
quotes  you  $60  per  thousand  feet,  less  trade  discounts  of  20  % 
and  5%  ;  another  firm  offers  you  the  same  lumber  at  $75  per 
thousand  feet,  less  33^%  and  8%.  The  terms  offered  by  both 
firms  are  ^/jo,  Vso-  ^^^  accept  the  better  offer  and  pay  cash. 
How  much  does  the  lumber  cost  you? 


COMMERCIAL  DISCOUNTS  195 

WRITTEN  REVIEW  TEST 
(Time,  approximately,  forty  minutes) 

1.  If  goods  are  bought  25%  below  the  list  price  and  sold  at 
the  list  price,  what  is  the  advance  per  cent  over  the  cost  ? 

2.  If  goods  are  bought  20  %  below  the  list  price  and  sold  at 
the  list  price,  what  is  the  advance  per  cent  over  the  cost  ? 

3.  If  goods  are  bought  10  %  below  the  list  price  and  sold  at  10  % 
above  the  list  price,  what  is  the  advance  per  cent  over  the  cost  ? 

4.  If  goods  are  bought  at  20%  and  12|%  below  the  list 
price,  and  sold  at  10%  below  the  list  price,  what  is  the  advance 
per  cent  over  the  cost  ? 

5.  A  hardware  dealer  bought  a  machine  listed  at  S24,  less 
16  J  %  and  10%,  and  sold  it  at  the  list  price.  At  what  per  cent 
above  cost  did  he  mark  the  selling  price  ? 

6.  A  jobber  wished  to  buy  at  such  a  discount  from  the  manu- 
facturer's list  price  that  he  could  make  an  advance  of  25%  over 
cost,  and  still  sell  at  the  manufacturer's  list  price.  What  would 
the  jobber  pay  for  $1000  worth  of  goods  ? 

7.  A  gentleman  wished  to  buy  a  carriage.  One  dealer  offered 
him  a  discount  of  33^%  and  10%  from  the  hst  price,  and  an- 
other dealer  offered  him  20%,  10%,  and  10%  from  the  list  price. 
If  the  hst  price  is  $450,  what  will  be  the  cost  of  the  carriage  if 
it  is  bought  at  the  better  discount  ? 

8.  Aug.  5,  you  buy  of  Gray,  Salisbury  &  Son,  New  York 
City,  4000  lb.  raisins  at  16/,  less  trade  discounts  of  25%,  20%, 
and  10%.  Terms:  Vio»  Vso-  You  pay  cash  for  freight  $3.20. 
If  you  pay  the  bill  Aug.  7,  what  will  the  raisins  cost  you  ? 

9.  You  desire  to  buy  200  lb.  nutmeg.  You  find  that  S.  S. 
Pierce  Co.,  of  your  city,  offer  this  article  at  75/  per  lb.,  less  a 
discount  of  25%,  and  that  Smith,  Perkins  &  Co.,  New  York 
City,  offer  it  at  70/  per  lb.,  less  discounts  of  15%  and  10%. 
The  freight  from  New  York  to  your  city  on  a  package  of  this 
kiod  is  $1.50.  The  terms  offered  by  both  firms  are:  Vio?  Vso* 
You  accept  the  better  offer  and  pay  cash.  How  much  does 
the  nutmeg  cost  you? 


CHAPTER  XV 

GAIN  AND  LOSS 
ORAL  EXERCISE 

1.  What  is  33|%  of  $660?  How  much  is  gained  on  goods 
bought  for  $900  and  sold  at  a  profit  of  331%  ? 

2.  What  per  cent  greater  is  $75  than  $60?  what  per  cent 
less  is  $60  than  $75?  Goods  bought  for  $100  are  sold  for 
$150.     What  is  the  gain  per  cent? 

3.  What  per  cent  less  is  $80  than  $100?  what  per  cent 
more  is  $100  than  $80?  Goods  bought  for  $100  are  sold  for 
$90.     What  is  the  loss  per  cent  ? 

4.  If  $800  is  increased  by  25%  of  itself,  what  is  the  result? 
Goods  bought  for  $1400  are  sold  at  a  profit  of  25%.  What  is 
the  selling  price  ? 

5.  If  $1500  is  decreased  by  331%  of  itself,  what  is  the 
result?  Goods  bought  for  $2700  are  sold  at  a  loss  of  331%. 
What  is  the  selling  price  ? 

6.  State  a  brief  method  for  finding  a  gain  of  6|^%;  a  gain 
of  6|%;  a  gain  of  8|^%;  a  gain  of  10%;  a  gain  of  1J%;  a  gain 
of  1|%;  a  gain  of  21%;  a  gain  of  31%. 

7.  State  a  brief  method  for  finding  a  loss  of  11^%;  a  loss 
of  121% ;  a  loss  of  14f  % ;  a  loss  of  16f  % ;  a  loss  of  20% ;  a  loss 
of  25%  ;  a  loss  of  9^^  %  ;  a  loss  of  371%. 

8.  State  a  brief  method  for  finding  a  gain  of  33 J%;  a  gain 
of  22|%;  a  gain  of  50%  ;  a  gain  of  66|%;  a  gain  of  75  %. 

203.  The  gains  and  losses  resulting  from  business  transac- 
tions are  frequently  estimated  at  some  rate  per  cent  of  the  cost, 
or  of  the  money  or  capital  invested. 

Since  no  new  principles  are  involved  in  this  subject,  illustrative  examples 
are  unnecessary. 

196 


GAIN  AND  LOSS 


197 


FINDING  THE   GAIN  OR  LOSS 


ORAL  EXERCISE 


By  inspection  find  the  gain  or  loss  : 


Per  Cent 
Cost       of  Gain 


Per  Cent 
Cost     of  Loss 


1.  $2900  50% 

2.  $1600  75% 

3.  $5600  28^% 

4.  $2700  331% 

5.  $2400  371% 

6.  $1400  42f% 

7.  $3200  621% 

8.  $2100  66|% 


9.  $1500  10% 

10.  $1600  1|% 

11.  $3000  1|% 

12.  $4800  21% 

13.  $3600  31% 

14.  $3200  6J% 

15.  $4500  6f% 

16.  $8400  81% 
25-48.   Find  the  selling  price  in  each  of 

WRITTEN  EXERCISE 


Per  Cent 
Cost       of  Gain 

17.  $7500      20% 

18.  $1400  25% 

19.  $2200  9J-^-% 

20.  $8100  111% 

21.  $6400  12|% 

22.  $2800  14f% 

23.  $9600  16|% 

24.  $3600  22|% 
the  above  problems. 


1.  An  importation  of  silks  invoiced  at  £  40  10«.  was  sold  at 
a  profit  of  25  % .  Find  the  amount  (in  United  States  money) 
of  the  gain. 

2.  An  importation  of  German  toys  invoiced  at  43,750  marks 
was  sold  at  a  gain  of  331  % .  Find  the  amount  (in  United  States 
money)  of  the  gain. 

3.  An  article  that  cost  $1  was  marked  10%  above  cost.  In 
order  to  effect  a  sale,  it  was  afterward  sold  for  10  %  below  the 
marked  price.     Find  the  gain  or  loss  on  250  of  the  articles. 

4.  A  man  bought  a  city  lot  for  $1150  and  built  a  house  on 
it  costing  $2650.  He  then  sold  the  house  and  lot  at  a  gain  of 
5  %.     How  much  did  he  gain  and  what  was  his  selling  price  ? 

5.  A  man  bought  a  quantity  of  silk  for  $450,  a  quantity  of 
fancy  plaids  for  $  120,  and  a  quantity  of  velvet  for  $  90.  He 
sold  the  silk  at  a  gain  of  25%,  the  plaids  at  a  loss  of  5  %,  and 
the  velvet  at  a  gain  of  331  % .  What  was  his  gain,  and  how 
much  did  he  realize  from  the  sale  of  the  three  kinds  of 
material  ? 


198  CONCISE   BUSINESS   ARITHMETIC 

FINDING  THE  PER  CENT  OF  GAIN  OR  LOSS 

ORAL  EXERCISE 
By  inspection  find  the  per  cent  of  gain  or  loss: 


Cost 

Gain 

Cost 

Loss 

^_„     Selling 
C^^^     Price 

Selling 
Price 

Gain 

1. 

$100 

$10 

7. 

$60 

$15 

13. 

$80   $90 

19. 

$300 

$60 

2. 

$150 

$50 

8. 

$40 

$10 

14. 

$90   $80 

20. 

$115 

$23 

3. 

$140 

$70 

9. 

$90. 

$45 

15. 

$60   $75 

21. 

$102 

$17 

4. 

$140 

$140 

10. 

$70 

$14 

16. 

$75   $60 

22. 

$420 

$60 

5. 

$200 

$400 

11. 

$80 

$16 

17. 

$10   $50 

23. 

$300 

$200 

6. 

$300 

$750 

12. 

$15 

$10 

18. 

$50  $10 

24. 

$700 

$100 

WRITTEN  EXERCISE 

1.  A  milliner  bought  hats  at  $  15  a  dozen  and  retailed  them 
at  $3  each.     What  per  cent  was  gained  ? 

2.  A  stationer  bought  paper  at  $  2  a  ream  and  retailed  the 
same  at  a  cent  a  sheet.     What  was  his  per  cent  of  gain  ? 

3.  A  dry-goods  merchant  bought  gloves  at  $7.50  a  dozen 
pair  and  retailed  them  at  $1.25  a  pair.  What  was  his  per  cent 
of  gain  ? 

4.  A  merchant  imported  50  gro.  of  table  knives  at  a  cost 
of  $1125.  Two  months  later  he  found  that  the  sales  of  table 
knives  aggregated  $920  and  that  the  value  of  the  stock  unsold 
was  $435.     Did  he  gain  or  lose,  and  what  per  cent  ? 

5.  An  importer  bought  a  quantity  of  silk  goods  for  £  400  5s. 
After  disposing  of  a  part  of  the  goods  for  $1200  he  took  an 
account  of  the  stock  remaining  unsold  and  found  that  at  cost 
prices  it  was  worth  $1047.82.  Did  he  gain  or  lose,  and  what 
per  cent? 

6.  Jan.  1,  F.  E.  Smith  &  Co.  had  merchandise  on  hand 
valued  at  $2500.  During  the  month  they  purchased  goods 
costing  $6000  and  sold  goods  amounting  to  $7500.  If  the 
stock -on  hand  at  cost  prices  Feb.  5  was  worth  $2500,  what 
was  the  per  cent  of  gain  on  the  sales  ? 


GAIN   AND  LOSS  199 


FINDING  THE   COST 


ORAL  EXERCISE 

JBy  inspection  find  the  cost : 
Loss      Rate  of  Loss 


1. 

1150 

10% 

2. 

$100 

li% 

3. 

1200 

11% 

4. 

$450 

^% 

5. 

1220 

6|% 

6. 

1115 

81% 

Selling 

Rate 

Price 

OF  Gain 

13. 

$1050 

5% 

14. 

$2040 

2% 

15. 

$3600 

20% 

16. 

$1400 

16|% 

17. 

$1800 

12^% 

18. 

$2400 

38*  % 

Gain    Rate  of  Gadt 

7. 

$35 

20% 

8. 

$79 

25% 

9. 

$12 

iH% 

10. 

$19 

16|% 

11. 

$44 

22|% 

12. 

$15 

331% 

Selling 

Rate 

Price 

OF  Loss 

19. 

$950 

6% 

20. 

$900 

50% 

21. 

$150 

H% 

22. 

$550 

16|% 

23. 

$240 

38J% 

24. 

$490 

22|% 

25.  A  man  bought  a  machine  for  S  240.48.  For  how  much 
must  he  sell  it  to  gain  12^  %  ? 

26.  B  sold  a  farm  for  S2400,  thereby  losing  25%.  For  how 
much  should  he  have  sold  it  to  have  gained  .10%  ? 

27.  By  selling  a  piano  at  $400  a  dealer  realizes  a  gain  of 
33^%.  What  would  be  the  selling  price  of  the  piano  if  sold 
at  a  gain  of  25  %  ? 

WRITTEN  EXERCISE 

1.  A  sleigh  was  sold  for  $64.80,  which  was  10  %  below  cost. 
What  was  the  cost  ? 

2.  An  office  safe  was  sold  at  $102,  which  was  20%  above 
cost.     What  was  the  cost  ? 

3.  A   merchant  marks  goods  16f  %  above  cost.     What  is 
the  cost  of  an  article  that  he  has  marked  $21.70? 


200  CONCISE   BUSINESS   ARITHMETIC 

4.  An  owner  of  real  estate  sold  2  city  lots  for  812,000  each. 
On  one  he  gained  25%  and  on  the  other  he  lost  25%.  What 
was  his  net  gain  or  loss  from  the  two  transactions  ? 

5.  A  merchant  sold  a  quantity  of  goods  to  a  customer  at  a 
gain  of  25%,  but  owing  to  the  failure  of  the  customer  he  re- 
ceived in  settlement  but  88)^  on  the  dollar.  If  the  merchant 
gained  $645.15,  what  did  the  goods  cost  him  ? 

6.  A  manufacturer  sold  an  article  to  a  jobber  at  a  gain  of 
25%,  the  jobber  sold  it  to  a  wholesaler  at  a  gain  of  20%,  and 
the  wholesaler  sold  it  to  a  retailer  at  a  gain  of  33^%.  If  the 
retailer  paid  $-28  for  the  article,  what  was  the  cost  to  manufac- 
ture it  ? 

7.  A  manufacturer  sold  an  article  to  a  wholesaler  at  a  gain 
of  20%,  the  wholesaler  sold  the  same  article  to  a  retailer  at  a 
gain  of  33J%,  and  the  retailer  to  the  consumer  at  a  gain  of 
25%.  If  the  average  gain  was  8  40,  what  was  the  cost  to 
manufacture  the  article  ? 

WRITTEN  REVIEW  EXERCISE 

1.  A  merchant  bought  goods  at  40  %  off  from  the  list  price 
and  sold  the  same  at  20  %  and  10  %  off  the  list  price.  What 
was  his  gain  per  cent  ? 

2.  I  bought  goods  at  50%  off  from  the  list  price  and  sold 
them  at  25  %  and  25  %  off  from  the  list  price.  Did  I  gain  or 
lose,  and  what  per  cent  ? 

3.  Apr.  15  you  bought  of  Baker,  Taylor  &  Co.,  Rochester, 
N.  Y.,  4000  bbl.  Roller  Process  flour  listed  at  $4.50  a  barrel, 
and  2000  bbl.  of  Searchlight  pastry  flour  listed  at  $4.75  a 
barrel.  Each  list  price  was  subject  to  trade  discounts  of  20% 
and  10  %.  You  paid  cash  $16,000  and  gave  your  note  at  30  da. 
for  the  balance.      What  was  the  amount  of  the  note  ? 

4.  May  18  you  sold  to  F.  H.  Clark  &  Co.,  New  York  City, 
2000  bbl.  of  the  Roller  Process  flour,  bought  in  problem  3,  at 
33J%  above  cost.  Terms:  Vio,  Vso-  ^'-  H.  Clark  &  Co. 
paid  cash.     Find  the  cash  payment. 


GAIN  AND  LOSS  201 

5.  May  30  you  sold  Smith,  Perkins  &  Co.,  Albany,  N.Y., 
the  balance  of  the  flour  bought  in  problem  3,  at  an  advance 
of  33J%  on  the  cost.  Terms:  Vio»  Vso-  The  flour  was  paid 
for  June  8.     Find  the  cash  payment. 

6.  What  is  the  net  gain  on  the  transactions  in  problems  3, 
4,  and  5  ?  the  net  gain  per  cent  ? 

7.  Dec.  15  you  bought  of  E.  B.  Johnson  &  Co.  400  bbl.  of 
apples  at  12.50  per  barrel.  Terms  :  Vio,  Vso-  You  paid  cash. 
Find  the  amount  of  your  payment. 

8.  May  15  you  sold  F.  E.  Kedmond  the  apples  bought  in 
problem  7,  at  |4  a  barrel.  Terms:  Vio?  Vso*  At  the 
maturity  of  the  bill  Redmond  refused  payment  and  you 
placed  the  account  in  the  hands  of  a  lawyer  who  succeeded  in 
collecting  75  %  of  the  amount  due.  If  the  lawyer's  fee  for  col- 
lecting was  4  %,  what  was  your  net  gain  or  loss  ? 

9.  A  tailor  made  25  doz.  overcoats  with  cloth  worth  f  2  a 
yard.  4  yd.  were  required  for  each  coat  and  the  cost  of 
making  was  $48  per  dozen.  He  sold  the  overcoats  so  as  to 
gain  33 J%.     How  much  did  he  receive  for  each  ? 

10.  Apr.  12  J.  D.  Farley  &  Son,  Trenton,  N.  J.,  bought  of 
Cobb,  Bates  &  Co.,  Boston,  Mass.,  a  quantity  of  green  Java 
coffee  sufficient  to  yield  2400  lb.  when  roasted.  If  the  loss  of 
weight  in  roasting  averages  4%,  what  will  the  green  coffee  cost 
at  30^  a  pound,  less  a  trade  discount  of  10%?  Arrange  the 
problem  in  bill  form. 

11.  If  the  coffee  in  problem  10  is  retailed  331%  above  cost, 
and  there  is  a  loss  of  1  %  from  bad  debts,  what  is  the  gain  on 
the  transactions  in  coffee  ?  the  gain  per  cent  ? 

12.  The  Metropolitan  Coal  Co.,  of  Boston,  Mass.,  decides 
to  bid  on  a  contract  for  supplying  2240  T.  of  coal  for  the  pub- 
lic schools  of  the  city.  It  can  buy  the  coal  at  $4.50  per  long 
ton  delivered  on  board  track,  Boston.  It  costs  on  an  average 
75^  per  short  ton  to  deliver  the  coal,  and  there  is  a  waste  of  ^  % 
from  handling.  Name  a  bid  covering  a  profit  of  20%.  Terms: 
cash. 


202  CONCISE   BUSINESS   AEITHMETIC 

FINDING   THE   PER   CENT   OF   GAIN  OR   LOSS 
ON   THE   SELLING   PRICE 

ORAL  EXERCISE 

1.  An  article  cost  S80  and  it  is  sold  for  $100.  What  is  the 
sum  gained  ?  The  gain  is  what  per  cent  of  the  cost  ?  of  the 
selling  price  ? 

2.  An  article  costs  $60  and  it  is  sold  for  $75.  What  is  the 
sum  gamed?  The  gain  is  what  per  cent  of  the  cost?  of  the 
selling  price  ? 

3.  An  article  is  sold  for  $  90.  If  the  gain  on  the  selling  price 
is  331  %,  what  was  the  cost,  and  what  is  the  gain  per  cent  on 
the  cost  price  ? 

204.    Find  by  inspection  the  gam  per  cent  on  the  selling  price : 


Cost 

Selling  Price 

Cost 

Selling  Price 

a,   $20 

$30 

/.    $120 

$150 

b.   $30 

$40 

g.   $125 

$150 

c.   $45 

$60 

k   $140 

$160 

d.   $60 

$75 

I   $150 

$175 

e.   $50 

$60 

y.   $160 

$180 

This  principle  may  be  applied  effectively  when  goods  have  been  marked 
by  a  merchant  at  a  certain  per  cent  on  the  advance  of  the  cost,  and  then 
marked  down  to  sell  at  cost. 

205.  If  an  article  that  costs  $  1  is  marked  to  sell  at  $  1.10,  what 
per  cent  of  reduction  will  restore  the  original  cost  price  ? 

Suggestion.  It  is  evident  that  a  reduction  of  10  %  on  the  selling  price 
will  not  restore  the  original  marking  of  $  1. 

206.  Find  by  inspection  the  per  cent  of  reduction  that  must 
be  made  to  reduce  the  marked  price  to  the  cost  price. 

Cost  Marked  Price  Cost  Marked  Price 

a.  $1.00  $1.25  d.   $1.50  $1.80 

b.  $1.25  $1.50  e,   $2.00  $2.50 

c.  $1.60  $2.00  /.   $3.00  $4.00 

207.  Business  men  are  continually  dealing  with  the  problem 
of  overhead  charges;  that  is,  the  cost  of  doing  business.   Overhead 


GAIN  AND   LOSS  203 

charges  include  such  expenses  as  employees'  salaries,  rent,  insur- 
ance, taxes,  light  and  heat,  postage,  advertising,  depreciation, 
telephone,  and  many  others.  To  the  invoice  charges  there  must 
be  added  a  certain  per  cent  to  cover  the  cost  of  doing  business. 
208.  The  followmg  principle  applies  to  subsequent  problems: 
Divide  the  invoice  cost  plus  the  freight  by  100  %  minus  the  over- 
head charges  plus  the  per  cent  of  profit  (100  %  —  charges  +  profits) ; 
the  result  will  be  the  selling  price.  (This  statement  is  based  on 
reckoning  the  overhead  expenses  and  the  gain  as  a  per  cent  of 
the  selling  price.) 

WRITTEN    EXERCISE 

1.  An  article  was  invoiced  at  $33.50;  freight  charges,  S1.50. 
If  the  overhead  charges  amounted  to  15  %  and  the  gain  to  10  %, 
what  was  the  selling  price  ? 

Solution.     15% +  10%  =  25%. 

100% -25%  =75%. 

$33.50  +  $  1.50  =  $35,  the  cost. 

$35  -T-  .75  =  $46.67,  the  selling  price. 
Proof.  25%  of  $46.67  =  $11.67,  overhead  charges  and  gain. 

$46.67-  $11.67  =  $35,  the  cost. 

2.  A  merchant  sold  goods  amounting  to  $  22,500.  If  the  over- 
head charges  amounted  to  18  %  and  the  profits  to  8  %,  what  was 
the  invoice  price  of  the  goods  if  the  freight  amounted  to  $  350  ? 

3.  A  merchant  marked  a  lot  of  goods  331  ^  above  cost,  but  as 
he  was  unable  to  sell  them  at  the  marked  price,  he  decided  to  reduce 
the  marking  to  cost.     "What  per  cent  reduction  must  be  made  ? 

4.  A  machine  was  invoiced  at  $53.50;  freight  charges,  $3.50. 
If  the  overhead  charges  of  the  business  amounted  to  20  %,  and 
the  gain  to  10  %,  what  must  be  the  selling  price  of  the  goods  ? 

5.  An  invoice  of  merchandise  amounted  to  $1204.50;  freight 
charges,  $  10.50.  If  the  overhead  charges  amounted  to  1 7J  %  and 
the  gain  to  7J  %,  what  must  be  the  selling  price  ? 

6.  A  merchant  marked  a  lot  of  goods  at  25  %  above  cost,  but 
as  the  goods  did  not  sell  at  the  marked  price,  he  reduced  it  25  %, 
and  announced  that  he  was  selling  at  cost.  What  per  cent  rep- 
resents the  amount  of  his  error?  If  the  goods  thus  marked 
cost  $1760.48,  what  did  the  merchant  lose  by  his  blunder? 


CHAPTER  XYI 

MARKING  GOODS 

209.  Merchants  frequently  use  some  private  mark  to  denote 
the  cost  and  the  selling  price  of  goods.  The  word,  phrase,  or 
series  of  arbitrary  characters  employed  for  private  marks  is 
called  a  key. 

Many  houses  use  two  different  keys  in  marking  goods,  one  to  represent 
the  cost  and  the  other  the  selling  price.  In  this  way  the  cost  of  an  article 
may  not  be  known  to  the  salesmen,  and  the  selling  price  may  not  be  known 
to  any  except  those  in  some  way  connected  with  the  business.  In  large 
houses,  when  but  one  key  is  used,  only  the  selling  price  is  indicated  on  the 
article,  it  being  deemed  best  to  keep  the  actual  cost  of  the  article  a  secret 
with  the  buyers.  In  small  houses,  when  but  one  key  is  used,  both  the  cost 
and  the  selling  price  are  frequently  written  on  the  article. 

210.  If  letters  are  used  to  mark  goods,  any  word  or  phrase 
containing  ten  different  letters  may  be  selected  for  a  key.  If 
arbitrary  characters  are  used,  any  ten  different  characters  may 
be  selected  for  a  key. 

Some  methods  of  marking  are  so  complicated  that  it  is  necessary  to 
always  have  a  key  of  the  system  at  hand  for  reference.  Goods  are  so  marked 
in  order  that  important  facts,  such  as  the  cost  of  goods,  may  be  kept  strictly 
private. 

211.  When  a  figure  is  repeated  one  or  more  times,  one  or 
two  extra  letters  called  repeaters  are  used  to  make  the  key 
word  more  secure  as  a  private  mark. 

212.  The  following  illustrates  the  method  of  marking  goods 
by  letters : 

Cost  Key  Selling-price  Key 

REPUBLICAN"  PERTHAMBOY 

1234567  8  90  1234567890 

Repeaters :  S  and  Z  Repeaters :  W  and  D 

204 


\_fUru_\ 


First  Cost 

OF 

Article  Freight 

Gain 

Loss 

First  Cost 

OF 

Article 

Freight 

Gain 

1.    12.50     10% 

20% 

5. 

116.00 

H% 

37|% 

2.    $1.00     10% 

20% 

6. 

$40.00 

6% 

16|% 

3.       .50 

33^% 

7. 

1  3.60 

nfo 

4.   14.80    20% 

25% 

8. 

$24.00 

MAEKING   GOODS  205 

The  cost  is  generally  written  above  and  the  selling  price  below  a  hori- 
zontal line  on  a  tag,  or  on  a  paster  or  box.  Gloves  No.  271, 
costing  ^5  a  dozen  and  selling  for  $6.25  a  dozen,  might  be 
marked  as  shown  in  the  margin.  Fractions  may  be  desig- 
nated by  additional  letters  or  characters.  Thus,  W  may  be 
made  to  represent  \,  K  ^,  etc.  in  the  above  key.  In  marking 
goods  for  the  retail  trade,  all  fractions  of  a  cent  are  called  another  whole  cent. 

WRITTEN    EXERCISE 

213.    Using  the  keys  given  in  §  212^  write  the  cost  and  the  selling 
price  in  each  of  the  following  problems : 


Loss 


10% 

214.  Using  the  following  keg,  write  the  cost  and  the  selling  price  in 
each  of  the  followiiig  problems  : 

Cost  Key  Selling-price  Key 

rL1JhHCDJ"+  T±unE3miui# 

1234567890  1234567890 

Repeaters:     Q        C^  Repeaters:     X         — 

First  Cost  First  Cost 

of  of 

Article   Charges    Gain  Loss  Article    Charges    Gain   Loss 

9.   $10.00       5%     20%  12.   $15.00      6|%      25% 

10.  $20.00     10%     50%  13.   $18.00      10%      25% 

11.  $30.00     6|%  25%         14.    $12.00        5%    331% 

215.  Wholesalers  and  jobbers  buy  and  sell  a  great  many 
articles  by  the  dozen.  Retailers  buy  a  great  many  articles  by 
the  dozen,  but  generally  sell  them  by  the  piece.  In  marking 
goods,  therefore,  it  is  highly  important  that  the  student  be  able 
to  divide  by  12  with  great  rapidity. 

To  divide  by  12  with  rapidity,  the  decimal  equivalents  of  the  12ths,  from 
T5  to  Tz  inclusive,  should  be  memorized. 


206 


CONCISE   BUSINESS   ARITHMETIC 


Table   op  Twelfths 


Twelfths 

Simplest 

Decimal 

Twelfths 

Simplest 

Decimal 

Form 

Value 

Form 

Vaute 

A 

$.08^ 

A 

$.581 

A 

J 

.16! 

A 

f 

.6Gf 

A 

i 

.25 

A 

f 

.75 

A 

i 

.331 

a 

t 

.83^ 

A 

.411 

H 

.911 

A 

i 

.50 

a 

1 

1.00 

216.  Example.  What  is  the  cost  of  one  shirt  when  a  dozen 
shirts  cost  $19? 

Solution.  Divide  by  12  the  same  as  by  any  number  of  one  digit  and  men- 
tally reduce  the  twelfths  in  the  remainder  to  their  decimal  equivalent.  Thus, 
say  or  think  1^^,  $1.58|,  practically  $1.58. 


ORAL   EXERCISE 
fState  the  cost  per  article  when  the  cost  per  dozen  articles  is 


1. 

$25.00. 

7. 

$7.00. 

13.    $23.20. 

19. 

$9.00. 

2. 

$37.00. 

8. 

$3.60. 

14.    $19.20. 

20. 

$7.00. 

3. 

$42.00. 

9. 

$2.40. 

15.   $66.60. 

21. 

$5.00. 

4. 

$64.00. 

10. 

$5.60. 

16.    $38.00. 

22. 

$7.50. 

5. 

$80.00. 

11. 

$3.40. 

17.    $17.00. 

23. 

$8.40. 

6. 

$13.00. 

12. 

$13.20. 

ORAL 

18.    $11.00. 

EXERCISE 

24. 

$17.50. 

1.  Hats  costing  $48  a  dozen  must  be  sold  for  what  price 
each  to  gain  25  %  ? 

2.  Rulers  bought  at  $2  a  dozen  must  be  retailed  at  how 
much  each  to  gain  50  %  ? 

3.  Note  books  costing  $1.60  per  dozen  must  be   retailed 
at  what  price  each  to  gain  121%  ? 

4.  Erasers  bought  at  $3.24  per  gross  must  be  retailed  at 
how  much  each  to  gain  111J%  ? 

5.  Matches  costing  $3.60  per  gross  boxes  must  be  retailed 
at  what  price  per  box  to  gain  100%  ? 


MAEKING  GOODS  207 

6.  Envelopes  bought  at  $2  per  M  must  be  sold  at  what 
price  per  package  of  25  to  gaiu  100%? 

7.  Pickles  bought  at  $1.80  per  dozen  bottles  must  be  sold 
at  what  price  per  bottle  to  gain  33  J  %  ? 

8.  Mustard  costing  $14.40  per  gross  packages  must  be  re- 
tailed at  what  price  per  package  to  gain  20%  ?  to  gain  50  %  ? 

LISTING  GOODS  FOR  CATALOGUES 

217.  In  listing  goods  for  catalogues  dealers  generally  mark 
them  so  that  they  may  allow  a  discount  on  the  goods  and  still 
realize  a  profit. 

218.  Example.  What  should  be  the  catalogue  price  of  an 
article  costing  $24  in  order  to  insure  a  gain  of  25  %  and  allow 
the  purchaser  a  discount  of  20  %  ? 

Solution.     ^  of  $24  =  $6,  the  gain. 

$30  =  the  selling  price,  which  is  20%  below  the  catalogue  price. 

.80  of  the  catalogue  price  =  $30. 

.%  the  catalogue  price  =  §30  -f-  .80  =  $37.50. 

WRITTEN  EXERCISE 

1.  At  what  price  must  you  mark  an  article  costing  $400  to 
gain  25  %  and  provide  for  a  20  %  loss  through  bad  debts  ? 

2.  What  should  be  the  catalogue  price  of  a  library  table 
costing  $25  in  order  to  insure  a  gain  of  20%  and  allow  the 
purchaser  a  discount  of  25  %  ? 

3.  You  list  tea  costing  30^  a  pound  in  such  a  way  that  you 
gain  33^  %  after  allowing  the  purchaser  a  trade  discount  of 
20  %.     What  is  your  list  price? 

4.  You  buy  broadcloth  at  $3.80  per  yard.  At  what  price 
must  you  mark  it  in  order  that  you  may  allow  your  cash 
customers  5  %  discount  and  still  realize  a  gain  of  20  %  ? 

5.  Having  bought  a  quantity  of  oranges  for  $3.00  per  C 
you  mark  them  so  as  to  gain  33 J  %  and  allow  for  a  20  %  loss 
through  bad  debts.  What  will  be  your  asking  price  per 
dozen? 


208 


CONCISE   BUSINESS   ARITHMETIC 


6.    At  what  price  must  the  articles  in  the  following  invoice 
be  listed  to  gain  20  %  and  allow  discounts  of  25  %  and  20  %  ? 

Boston,  Mass,,         Nov.    24,    19 

Mv.   Edgar  C.  Townsend 

Rochester,  N.Y. 

Bought  of  WELLS,  FOWLER  &  CO. 

Terms  Net  SO  da. 


#721 
#924 


50 
25 


18.00 
12.00 


Oak  Bookcases 
Gentlemen *s  Chiffoniers 

Less  IO5J 

WRITTEN  REVIEW  EXERCISE 


400 
300 


700 
70 


630 


1.  Using  the  word  importance^  with  repeaters  s  and  w^  for 
the  buying  key,  and  the  words  huy  for  cash^  with  repeaters  t 
and  w,  for  the  selling  key,  write  the  cost  and  selling  price  of 
the  articles  in  the  following  bill.  It  is  desired  to  gain  25  %  on 
the  pens  and  pencils,  20  %  on  the  cards,  and  to  provide  for  a 
loss  of  12|  %  through  bad  debts. 

Boston,  Mass.,       Oct.   18,   19 

Messrs.  WHITE  &  WYCKOPP 

Holyoke,   Mass. 

Bought  of  C.  E.  Stevens  &  Co. 

Terms  Net  30  da. 


100 
25 

50 


gro.    Pens  |0.80 

«»  Lead  Pencils  5.20 

pkg.  Record  Cards  .40 

Less  12  1/251 


80 
80 
20 


180 
22 


50 


157 


50 


CHAPTER  XYII 

PROPERTY  INSURANCE 
riEE   INSURANCE 

ORAL   EXERCISE 

1.  One  hundred  persons  have  property  valued  at  S  500,000. 
They  pay  into  a  common  fund  60/  per  S 100  of  this  sum.  What 
is  the  amount  of  the  fund  ? 

2.  These  one  hundred  persons  live  in  widely  separated  parts 
of  the  country.  Is  it  likely  that  many  of  them  will  suffer  losses 
by  fire  in  the  same  year  ? 

3.  Suppose  the  losses  to  this  property  by  fire  for  a  year  amount 
to  S2500.  What  portion  of  the  common  fund  will  remain  on 
hand  as  a  surplus  ?     (No  interest.) 

4.  If  this  surplus  is  divided  among  the  hundred  persons  at  the 
end  of  the  year,  how  much  should  A,  who  paid  in  $  30,  receive  ? 

5.  What  are  the  companies  organized  to  receive  and  distribute 
the  fund  in  problem  1  called  ? 

219.  Insurance  is  a  contract  whereby  for  a  stipulated  con- 
sideration one  party  agrees  to  indemnify  another  for  the  loss  or 
damage  on  a  specified  subject  by  specified  perils,  according  to 
certain  prescribed  terms  and  conditions. 

The  best-known  forms  of  property  insurance  are  fire  insurance  and 
marine  insurance. 

There  are  also  property-insurance  companies  which  insure  against  loss 
due  to  steam-boiler  explosions,  failure  of  crops,  death  of  live  stock,  burglary, 
injury  to  business  by  strikes  among  employees,  and  numerous  other  hazards. 

220.  Fire  insurance  is  insurance  against  loss  of  property  or 

damage  to  it  by  fire. 

A  contract  of  fire  insurance  frequently  covers  loss  by  lightning  or  tornado. 
It  also  covers  damage  resulting  from  or  consequent  on  a  fire,  such  as  the  loss 


210  CONCISE   BUSINESS   ARITHMETIC 

resulting  from  water  applied  for  the  purpose  of  extinguishing  flames, 
also,  for  the  loss  when  such  destruction  has  been  ordered  by  the  proper 
authorities. 

221.  The  insurer,  also  called  the  underwriter,  is  the  one  who 
agrees  to  indemnify.  The  insured  is  the  one  to  whom  the 
promise  of  indemnity  is  made.  The  premium  is  the  considera- 
tion agreed  upon  to  be  paid  by  the  insured.  The  policy  is  the 
written  contract  between  the  insurer  and  the  insured. 

222.  Fire  insurance  is  usually  conducted  under  the  joint  stock 
or  the  mutual  plan. 

In  a  joint  stock  company  capital  is  subscribed,  paid  for,  and  owned  by- 
persons  called  stockholders,  who  share  in  the  gains  and  are  liable,  to  the 
extent  of  their  subscriptions,  for  all  the  losses. 

A  mutual  insurance  company  is  one  in  which  all  the  policy  holders  share 
the  gains  and  bear  the  losses  in  proportion  to  the  amount  of  the  premiums 
they  pay  to  that  particular  company,  and  their  fire  funds  consist  of  the 
reserve  earnings  and  the  results  of  investments. 

223.  Policies  of  insurance  are  of  various  kinds.  The  ordinary 
policy  is  a  contract  of  indemnity,  that  is,  a  contract  in  which  the 
amount  paid  in  case  of  loss  does  not  exceed  a  certain  specified 
sum ;  this  sum  is  determined  by  evidence  after  the  loss  occurs. 
A  valued  policy  is  one  that  states  in  advance  the  amount  to  be 
paid  in  case  of  loss. 

Further  subdivisions  of  policies  are  as  follows :  specific^  one  that  covers 
a  particular  kind  of  property,  as  a  single  building ;  blanket,  one  that  covers 
several  items  of  property,  as  a  group  of  buildings  and  the  contents ;  Jixed, 
one  that  covers  property  at  some  particular  defined  location ;  floating,  one 
that  covers  specified  property  while  in  transit  or  in  various  defined  locali- 
ties ;  open,  one  which,  while  it  affixes  the  extreme  limit  of  the  amount  and 
duration  of  the  risk,  is  yet  open  to  secure  endorsements  granting  insurance 
in  various  amounts  and  places  at  any  time  and  for  any  period  that  may  be 
agreed  upon  at  the  time  of  the  endorsement ;  this  policy  is  used  largely  to 
protect  such  stocks  as  grain  in  elevators  or  as  the  contents  of  warehouses, 
and  the  records  are  usually  kept  in  a  book  known  as  an  open  policy  book. 

224.  The  standard  forms  of  contract  used  in  fire  insurance 

policies  are  prescribed  by  the  state. 

These  forms  not  only  define  the  maximum  amount  and  the  term  for 
which  the  company  is  liable  but  also  the  consideration  paid  by  the  insured. 


PKOPERTY  INSURANCE  211 

the  conditions  under  which  the  contract  will  become  void,  the  methods 
to  be  followed  in  the  settlement  of  a  loss,  and  the  procedure  to  effect  the 
cancellation  of  the  contract. 

If  a  loss  either  total  or  partial  occurs  under  such  a  policy,  the  company- 
is  bound  to  pay  only  so  much  of  the  sum  stated  in  the  policy  as  will  in- 
demnify the  insured;  e.g.  if  a  building  insured  for  $3000  is  damaged  by 
fire  $400,  only  the  actual  loss,  $400,  can  be  recovered;  but  if  the  same 
building  were  damaged  by  fire  $3500,  the  company  could  not  be  held  for 
more  than  $3000,  the  sum  stated  in  the  policy. 

225.  Average  and  co-insurance  clauses.  "Where  a  number  of 
detached  properties  are  insured  under  one  policy,  it  is  customary 
to  attach  what  is  known  as  an  average  clause  which  specifies  that 
the  amount  of  insurance  covering  any  one  particular  piece  of 
property  shall  bear  such  proportion  to  the  total  amount  of  insur- 
ance on  the  whole  as  the  value  of  that  special  piece  of  property 
bears  to  the  value  of  all  of  the  properties  so  covered. 

226.  Many  fire-insurance  policies  contain  what  is  known  as  a 
co-insurance,  or  a  reduced-rate,  clause.  Under  this  clause  the 
insured  party  agrees  to  keep  his  property  insured  for  a  certain 
percentage  of  its  value ;  failing  to  do  this,  the  company  or  com- 
panies insuring  him  are  liable  only  for  that  proportion  of  a  loss 
which  the  amount  they  insure  bears  to  the  specified  percentage 
of  the  sound  value  of  the  property  covered. 

Thus,  the  value  of  a  piece  of  property  is  $  10,000,  and  the  insured  agrees 
to  keep  it  insured  for  80%  of  its  value,  or  $8000,  but  fails  to  do  so  and 
carries  only  $0000  insurance.  Should  a  loss  occur,  the  company  will  pay 
only  three  fourths  (f  ^^^)  of  the  amount  of  such  loss. 

227.  The  rate  in  fire  insurance  is  the  amount  to  be  paid  to 
secure  S 100  of  indemnity  for  one  year. 

The  rate  is  based  on  the  character  of  the  risk ;  the  greater  the  likeli- 
hood of  fire  the  higher  the  rate. 

When  policies  are  written  for  a  period  of  more  than  one  year,  a  reduc- 
tion is  usually  made  in  figuring  the  premium.  Illustrations  :  on  city  dwell- 
ings the  premium  for  five  years  is  charged  for  four  times  the  annual  rate ; 
if  written  for  three  years,  for  two  and  one-half  times  the  annual  rate. 

Rates  are  expressed  by  the  number  of  cents  charged  for  $  100  of  insurance. 
When  over  $1  per  hundred,  the  rate  is  often  stated  in  dollars  and  cents. 

Short  rates  are  those  used  for  a  term  of  less  than  one  year ;  they  are 
proportionately  higher  than  the  annual  rates. 


212  CO]^CISE   BUSINESS   ARITHMETIC 


ORAL  EXERCISE 

1.  What  is  the  cost  of  S6500  insurance  at  80/  per  SlOO? 

2.  What  is  the  premium  on  a  S 4000  policy  at  S1.50  per  SlOO  ? 

3.  What  is  the  cost  of  S6000  insurance  at  75/  per  SlOO  ? 

4.  B  insures  a  S6000  bam  for  |  value  at  50/  per  SlOO. 
What  quarterly  premium  should  he  pay  ? 

5.  A  insures  a  S6000  house  for  |  value,  at  50/  per  SlOO. 
What  is  the  semiannual  premium  ? 

6.  Goods  worth  S3000  are  insured  for  |-  value.  If  the 
annual  premium  is  S  30,  what  is  the  rate  ? 

7.  I  insure  S  2400  worth  of  merchandise  for  |  of  its  value  at 
60/  per  SlOO.     What  premium  must  I  pay? 

8.  I  insure  a  stock  of  goods  worth  S8000  for  S6000  at  2%. 
The  goods  become  damaged  by  fire  to  the  extent  of  S3000. 
Under  an  ordinary  policy  how  much  can  I  recover  ?  What  will 
be  my  net  loss,  premium  included  ? 

9.  A  brick  schoolhouse  is  insured  at  50/  per  SlOO,  the 
annual  premium  is  S50,  and  the  face  of  the  policy  |  of  the 
value  of  the  building.    What  is  the  value  of  the  building? 


ORAL    EXERCISE 

^ta 

te  the  premium  in  each  of  the  following  problems : 

Facb 

Face 

OF  POLICT 

Rate 

OF  Policy 

Rate 

1. 

S1600 

mo 

3.    S3500 

Sl.lO 

per 

SlOO 

2. 

$1000 

ii% 

4.   $5000 

S1.20 

per 

SlOO 

State  the  face  of  the  policy  in  each  of  the  following  problems  : 
Premium  Rate  Premium  Rate 

5.  S9  2%  7.   S  13.50        S1.35  per  SlOO 

6.  S15  11%  8.   S24.00         S1.60  per  SlOO 

State  the  rate  of  insurance  in  each  of  the  following  problems : 


Face 

Face 

OF  Policy 

Premium 

OF  Policy 

Premium 

9.   SI 700 

S  25.50 

11.    S3200 

$130.00 

10.   $1850 

$37.00 

12.   $6500 

$40.00 

PEOPEETY   iNSiTRAjSTCE  ^13 

228.  The  following  is  an  extract  from  a  tariff,  or  rate,  book  for 
the  properties  shown  on  the  map  which  follows  this  schedule. 

MAIN  STREET,   SOUTH   SIDE 

No.  Flat  Rate  80%  Ratk 

189  John  Smith  &  Co. 

Frame  carriage  factory  $1.75  c  $1.23  c 

Contents  1.75  c  1.23  c 

193  John  Smith 

Frame  dwelling  $0.25  a               

197               Frame  stable  (private)  1.00  a                

199  William  Brown 

Frame  store  and  dwelling  $0.40  c  $0.28  c 

Contents  of  grocery  store  0.40  c  0.28  c 

Contents  of  dwelling  0.40  a  0.28  c 

203-205  James  Robinson 

Brick  mercantile  building  $0.70  a  $0.50  a 
Robinson  &  Co. 

Department  store  $0.70  c  $0.50  c 

Offices  second  and  third  floors  0.70  c  0.50  c 

STATE   STREET,   KORTH   SIDE 

244  James  Green 

Brick  store  and  dwelling  $0.25  a  $0.17^  a 
National  Butter  Co.  0.25  c  0.17^  c 
Dwelling  0.25  c  

248  Thomas  White 

Frame  stable  $1.00  c  $0.70  c 

White's  Livery  .        1.00  c  0.70  c 

252  Thomas  White 

Frame  dwelling  and  contents  $0.25  a  $0.17^  a 

256  Town  of  Jonesville 

Brick  high  school  $0.50  a  $0.35  a 

Contents  .  0.50  a  0.35  a 

258  Samuel  Parker 

Brick  dwelling  $0.17  a  $0.12  a 

260        .  State  Street  Baptist  Society 

Brick  church  building  $0.50  a  $0.35  a 

Organ  and  other  contents  0.50  a  0.35  a 

The  letter  a  after  the  rate  indicates  that  the  insurance  on  this  property  can 
be  written  for  more  than  one  year ;  that  is,  at  two  and  one-half  times  the  rate, 
for  a  three-year  policy,  and  at  four  times  the  rate,  for  a  five-year  policy. 

The  letter  c  after  the  rate  indicates  that  the  insurance  on  this  property  can 
be  written  for  one  year,  or  for  a  number  of  years,  at  yearly  rates. 

The  city  block,  page  214,  contains  properties  insured  under  the  above 
schedule  of  rates. 


214 


CONCISE   BUSINESS   AEITHMETIC 


J 


Diagram  op  a  City  Block 


Main  Street 

103  197  199 


244  248  262  256 

State  Street 


n  [ 


r 


WRITTEN   EXERCISE 


These  problems  apply  to  tlie  properties  shown  on  the  above 
diagram ;  also  to  the  tariff  of  rates  in  the  preceding  schedule. 
The  flat  rate  is  used  unless  the  co-insurance  clause  is  mentioned. 

1.  The  frame  carriage  factory  at  189  Main  Street  is  worth 
$7000.  The  contents  are  worth  $8000 ;  both  are  insured  at  -f 
of  their  value.     What  is  the  amount  of  the  annual  premium  ? 

2.  The  frame  dwelling  at  193  Main  Street  is  worth  $  3400,  and 
the  contents,  $1200.  The  frame  stable  owned  by  the  same  party 
at  197  Main  Street  is  worth  $1500,  and  the  contents,  $1100. 
All  of  this  property  is  insured  for  1  yr.  at  a  |  valuation.  What 
is  the  annual  premium  ?    What  will  it  cost  to  insure  it  for  3  yr.  ? 

3.  The  store  and  dwelling  at  199  Main  Street  are  worth  $4800. 
The  contents  of  the  store  are  worth  $2400,  and  of  the  dwelling, 
$800.    What  will  it  cost  to  insure  the  property  for  1  yr.? 

4.  The  brick  mercantile  building  at  203—205  Main  Street  is 
worth  $20,000.  The  contents  of  the  first  floor  are  worth  $4500, 
and  of  the  second  Eind  third  floors,  $  7500.  All  are  insured  at  a 
75%  valuation  for  1  yr.  What  is  the  amount  of  the  premium? 
A  fire  occurs,  and  the  building  and  the  contents  are  damaged  to  the 
extent  of  $4500.  If  the  policies  contained  an  80%  co-insurance 
clause,  how  much  will  the  insuring  company  have  to  pay  ? 


PKOPEllTY   mSURAi^CE  215 

5.  Suppose  that  the  buildmg  described  in  problem  4  was 
insured  in  Company  A  for  $  18,000  at  the  tariff  rate,  and  the  con- 
tents in  Company  B  for  S  10,000  at  a  rate  of  75/;  that  each 
company  had  an  80  %  co-insurance  clause  attached  to  its  policy ; 
that  the  building  was  damaged  to  the  extent  of  $  3000,  and  the 
contents,  $  2500.  How  much  would  each  company  have  to  pay  ? 
What  would  be  the  net  loss  to  the  owner  of  the  building  ?  to  the 
owner  of  the  contents?  (Premium  included  in  each  case,  but 
no  interest.) 

6.  The  brick  church  at  260  State  Street  is  worth  $10,000, 
and  the  contents,  $3500.  The  property  is  insured  for  1  yr.  for 
$  8100.  If  the  policy  contains  an  80  %  co-insurance  clause,  what 
is  the  net  loss  to  the  insurance  company  (premium  included)  if 
the  property  is  wholly  destroyed  by  fire  ? 

7.  If  the  brick  school  building  at  256  State  Street  is  worth 
$15,000  and  the  contents  are  worth  $7500,  what  will  it  cost 
under  the  term  rule  to  insure  it  for  5  yr.  for  80  %  of  its  value  ? 

8.  For  insuring  the  frame  buildings  at  252  and  248  State 
Street,  and  the  contents  of  each  for  ^  of  their  value,  the  owner 
pays  an  annual  premium  of  $  22.50.  If  the  frame  stable  and  the 
contents  are  worth  |-  of  the  frame  dwelliug  and  the  contents,  what 
is  the  value  of  each  building,  includiug  the  contents  ? 

9.  The  brick  store  and  the  dwelliug  at  244  State  Street  are 
worth  $15,000 ;  the  property  is  insured  in  three  companies  for  ^ 
of  its  value.  Company  A  carries  i  of  the  line  at  the  tariff  rate ; 
Company  B,  |  of  the  line  at  a  50  /  rate ;  Company  C,  the  re- 
mainder of  the  line  at  a  66|  /  rate.  What  is  the  total  premium 
paid  ?  The  building  is  damaged  by  fire  to  the  amount  of  $6000. 
What  amount  will  each  company  pay  ? 

10.  I  insured  a  block  of  buildings  in  the  ^tna  Insurance 
Company  for  $75,000  at  an  annual  rate  of  75/.  The  ^tna 
afterwards  reinsured  $15,000  of  its  liability  under  my  policy  in 
the  Continental  Insurance  Company  at  75/,  and  $20,000  in  the 
German  American  Insurance  Company  at  the  same  rate.  The 
buildmg  was  damaged  by  fire  $  20,000.  What  was  the  net  loss 
pf  each  of  the  three  companies  ? 


INTEREST   AND   BANKING 
CHAPTER  XYIII 

INTEREST 
ORAL  EXERCISE 

1.  A  borrows  $100  of  B  for  1  yr.  At  the  end  of  the  year 
what  will  A  probably  pay  B  besides  the  face  of  the  loan  ? 

2.  C  puts  $100  in  a  savings  bank  and  leaves  it  for  1  yr. 
What  can  he  draw  out  at  the  end  of  the  year  besides  the 
money  deposited  ? 

3.  If  you  wished  to  borrow  money  of  a  bank  in  your  town, 
what  rate  of  interest  would  you  have  to  pay  ? 

4.  If  you  loaned  a  man  $  500  for  1  yr.,  what  would  you 
require  him  to  give  you  as  evidence  of  the  loan  and  security 
for  its  payment  ?  ~ 

229.  The  compensation  paid  for  the  use  of  money  is  called 
interest.  Interest  is  computed  at  a  certain  per  cent  of  the  sum 
borrowed.  This  per  cent  of  interest  is  called  the  rate,  and  the 
sum  upon  which  it  is  computed,  the  principal. 

The  rate  of  interest  allowed  by  law  is  called  the  legal  rate.  Persons  may 
agree  to  pay  less  than  this  rate,  but  not  more,  unless  a  higher  rate  by  special 
agreement  is  permitted  by  statute.  When  an  obligation  is  interest-bearing 
and  no  rate  is  mentioned,  the  legal  rate  will  be  understood.  An  agreement 
for  interest  greater  than  that  allowed  by  law  is  called  usury. 

230.  In  the  commercial  world,  12  mo.  of  30  da.  each,  or  360 
da.,  are  reckoned  as  1  yr. 

This  method  is  not  exact,  but  it  is  the  most  common  because  the  most 
convenient.  It  has  been  legalized  by  statute  in  some  states  and  is  gener- 
ally used  in  all  the  states. 

216 


INTEREST  217 

SIMPLE   INTEREST 
The  Day   Method 

oral  exercise 

1.  How  many  days  in  a  commercial  year  ? 

2.  What  part  of  a  year  is  60  da.  ?  6  da.  ?  What  is  the  interest 
on  II  for  1  yr.  at  6 %  ?  for  60  da.  ?  for  6  da.  ? 

3.  How  do  you  find  .01  of  a  number?  .001  of  a  number? 
What  is  the  interest  on  $120  for  60  da.  at  6  %  ?  for  6  da.  ? 

4.  State  a  short  method  for  finding  the  interest  on  any  prin- 
cipal for  60  da.  at  6  %  ;   for  6  da. 

5.  1  da.  is  what  part  of  6  da.  ?  What  is  ^  of  .001  ?  What  is 
the  interest  on  11200  for  1  da.  at  6  %  ?  on  $180  ?  on  $1500  ? 

6.  State  a  short  method  for  finding  the  interest  on  any 
principal  for  1  da.  at  6  % . 

231.  In  the  foregoing  exercise  it  is  clear  that  0.001  of  any 
principal  is  equal  to  the  interest  for  6  da.  at  6%;  or  0.001  of  any 
principal  is  equal  to  6  times  the  interest  for  1  da,  at  6^0- 

ORAL  EXERCISE 

1.  Find  the  interest  on  each  of  the  following  for  6  da.  at  6%. 
a.  $250.  e.  $560.  i.  $678.  m,  $290.  q.  $890. 
h.    $870.         /.    $435.       j,    $320.        n.    $150.       r.    $750. 

c,  $358.         g.    $430.       k.    $100.        o.    $325.       s.    $580. 

d.  $350.         h,    $470.        I    $185.       p.    $990.       t,    $625. 

2.  Find  the  interest  on  each  of  the  above  amounts  for  12 
da.  at  6  %  ;  for  18  da. ;  for  24  da. 

3.  Find  tlie  interest  on  each  of  the  following  for  1  da.  at  6%. 
a.  $360.  e.  $660.  i.  $600.  m.  $480.  q.  $840. 
5.  $450.  /.  $900.  j.  $180.  n.  $780.  r.  $200. 
c.  $300.  g.  $540.  h.  $720.  o.  $400.  s.  $330. 
6?.    $420.         h.   $240.        Z.    $500.       ^.    $120.       t,    $960. 

4.  Find  the  interest  on  each  of  the  above  amounts  for 
3  da.  at  6  %  ;  for  2  da. 


218  CONCISE   BUSINESS   ARITHMETIC 

232.   Example.     Find  the  interest  on  $450  for  54  da.  at  6  %. 

Solution.    Pointing  off  three  places  to  the  left     54  x  $0.45  =  $24.30 
gives   $0.45,   or  6  times  the   interest   for   1    da.      ^94  30 -=- 6  =  S4  05 
Multiplying  this  result  by  54  gives  $24.30,   or  6 

times  the  interest  for  54  da.     Dividing  this  result  by  6  gives  $4.05,  the  required 
interest.  9 

By    arranging    the    numbers    as  shown    in    the      54  X  $0.45 
margin  and   canceling    the  work  is  greatly  short-  ■-*  =$4.05 

ened. 

WRITTEN  EXERCISE 


f 


At  6^0  find  the   interest   on   each   of  the  following  problems. 
Reduce  the  time  expressed  in  months  and  days  to  days. 


Principal    Time 

Principal    Time 

Principal          Time 

1. 

$620  54  da. 

7. 

$900.00  29  da. 

13. 

$375.80  2  mo.  15  da. 

2. 

$175  84  da. 

8. 

$865.45  93  da. 

14. 

$300.00  3  mo.  19  da. 

3. 

$645  42  da. 

9. 

$700.00  96  da. 

15. 

$171.15  1  mo.  14  da. 

4. 

$300  84  da. 

10. 

$974.30  62  da. 

16. 

$120.00  4  mo.  14  da. 

5. 

$600  72  da. 

11. 

$178.45  40  da. 

17. 

$211.16  6  mo.  16  da. 

6. 

$502  66  da. 

12. 

$438.55  50  da. 

18. 

$665.65  1  mo.  10  da. 

ORAL  EXERCISE 

1.  What  is  the  interest  on  $800  for  6  da.  at  3  %  ? 

Solution.     80^  is  the  interest  for  6  da.  at  6  %.    3%  is  \  of  6%;  therefore, 
\  of  80)^,  or  40  <P,  is  the  interest  for  6  da.  at  3%. 

2.  If  the  interest  at  6%  is  $45,  what  is  the  interest  for  the 
same  time  at  3%  ?  at  12%?  at  2%  ?  at  1%  ?  at  1^%? 

3.  Formulate  a  short  method  for  changing  6%  interest  to 
8%  interest. 

Solution.     8  %  is  ^  more  than  6  % ;  hence,  the  interest  at  6%  increased  by 
I  of  itself  equals  the  interest  at  8%. 

4.  State  a  short  method  for  changing   6%  interest  to  7% 
interest;  to  5%  ;  to  9%  ;  to  71%  ;  to  41%. 

5.  If  the  interest  at  6%  is  $120,  what  is  the  interest  at  7%? 
at  5%?  at  8%?     at  4%  ?  at  7i%?  at  41% ? 


INTEREST  219 

233.  In  the  foregoing  exercise  it  is  clear  that  6  %  interest  in- 
creased by  ^  of  itself  equals  9  %  interest;  hy  \  of  itself  8  %  interest; 
^y  \  of  itself  7\^o  interest;  hy  \  of  itself  7%  interest;  also  that 

6ffo  interest  decreased  hy  i  of  itself  equals  4  (fo  interest;  hy  \of 
itself  41  %  interest;  hy  J  of  itself  5%  interest;  also  that 

6%  interest  divided  hy  2  equals  3%  interest;  hy  3^  2(fo  inter- 
est; hy  6,  1%  interest;  hy  4,  i|  %  interest, 

6  %  interest  multiplied  by  2  equals  12  %  interest. 

6  %  interest  is  clianged  to  10  %  interest  by  dividing  by  6  and  removing 
the  decimal  point  one  place  to  the  right;  to  any  other  rate  by  dividing 
by  6  and  multiplying  by  the  given  rate. 

WRITTEN  EXERCISE 

Using  the  exact  numher  of  days^  find  the  interest  on  : 

1.  $2500  from  Sept.  18,  1915,  to  Feb.  6,  1916,  at  9%;  at 
^%',  Sit  4:%;  at  3%. 

2.  $1700  from  Nov.  20,  1915,  to  Jan.  16,  1916,  at  8% ;  at 
21%  ;  at  51%;  at  31%;  at  4%. 

3.  $  2750  from  Dec.  16, 1915,  to  Jan.  17, 1916,  at  7  % ;  at  2  %  ; 
at  4  %  ;  at  5 %  ;  at  1  %  ;  at  10 %. 

4.  16250  from  Dec.  18,  1915,  to  Feb.  6,  1916,  at  71%;  at 
10%;  at  11%;  at  4|%;  at  9%;  at  8%;  at  7%;  at  3%. 

The  Banker's  Sixty-Day  Method 
oral  exercise 

1.  60  da.  (2  mo.)  is  what  part  of  a  commercial  year? 

2.  What  is  the  interest  on  $1  for  2  mo.  at  6%  ?  for  60  da.? 

3.  How  can  you  find  0.01  of  a  number?  What  is  the  interest 
on $50  for  60  da.  at  6%?  on $370?  on  $590?  on  $214.55? 

4.  What  fractional  part  of  60  da.  is  30 da.?  20  da.  ?  15  da.  ? 
10  da.  ?  What  is  the  interest  on  $1680  for  60  da.  ?  for  30  da.  ? 
for  20  da.  ?  for  15  da.  ?  for  10  da.  ? 

5.  State  a  simple  way  to  find  the  interest  on  any  principal 
for  60  da.  at  6%;  for  30  da.;  for  20  da.;  for  15  da.;  for 
10  da. 

CB 


220  CONCISE   BUSINESS   ARITHMETIC 

6.    Read  aloud  the  following,  supplying  the  missing  words 
a.  60  da.  minus  ^^  of  itself  equals  55  da. ;   60  da.  minus 


of  itself  equals  50  da. ;  60  da.  minus of  itself  equals  40 

da.  ;  60  da.  minus  • of  itself  equals  45  da. 

h.    60  da.  plus  ^^2"  ^^  itself  equals  65  da. ;  60  da.  plus 

of  itself  equals  70  da. ;   60  da.  plus of  itself  equals  75  da. ; 

60  da.  plus of  itself  equals  80  da. ;  60  da.  plus of 

itself  equals  90  da. 

7.  What  is  the  interest  on  $600  for  60  da.  at  6%?  for 
bb  da.  ?  for  50  da.  ?  for  40  da.  ?  for  45  da.  ? 

8.  What  is  the  interest  on  $1200  for  60  da.?  for  65  da.? 
for  70  da.  ?  for  75  da.  ?  for  80  da.  ?  for  90  da.  ? 

9.  State  a  short  way  to  find  the  interest  at  6%  for  80  da. ; 
for  90  da. ;  for  50  da. ;  for  ^b  da. ;  for  55  da. ;  for  75  da. ;  for 
70  da. ;  i^  40  da. ;  for  45  da. 

234.  In  the  above  exercise  it  is  clear  that  removing  the 
decimal  'point  two  places  to  the  left  in  the  principal  gives  the 
interest  for  60  da.  at  6<^o* 

235.  Examples,  l.  Find  the  interest  on  $1950  for  20  da. 
at  6%. 

Solution.  Removing  the  decimal  point  two  places  to  the  left  $19.50 
gives  the  interest  for  CO  da.  20  da.  is  \  of  60  da.  \oi%  19.50  =  ~^6~50 
$6.50.  •  ' 

2.    What  is  the  interest  on  $8400.68  for  75  days  ? 

Solution.     Removing  the  decimal  point  two       $84.0068 
places  to  the  left  gives  the  interest  for  60  da.  ^-j  ^/%^  «- 

75  da.  is  60  da.  increased  by  \  of  itself  ;  therefore,      * 

$84.0068  increased  by  \  of  itself  or  $105.01  is  $105.0085,  or  $105.01 
the  required  interest.  In  the  following  exercise  determine  the  separate  interest 
mentally  whenever  it  is  possible  to  do  so. 

WRITTEN  EXERCISE 

1.    Find  the  total  amount  of  interest  at  6%  on: 
$8400  for  60  da.  $8400  for  12  da.  $7900  for  20  da. 

$8400  for  30  da.  $8400  for  10  da.  $7900  for  15  da. 

$8400  for  20  da.  $7900  for  60  da.  $7900  for  12  da. 

$8400  for  15  da.  $7900  for  30  da.  $7900  for  10  da. 


INTEREST  221 

2.  Find  the  total  amount  of  interest  at  6%  on: 

$  1600  for  60  da.  $  1600  for  40  da.  1 2800  for  75  da. 

i  1600  for  55  da.  $  2800  for  60  da.  $  2800  for  80  da. 

1 1600  for  50  da.  $  2800  for  65  da.  $  2800  for  90  da. 

$  1600  for  45  da.  $  2800  for  70  da.  $  7200  for  55  da. 

3.  Find  the  total  amount  of  interest  at  6  %  on  : 

$  1500.60  for  30  da.  $  832.60  for  90  da.  1 8575.65  for  70  da. 
$  1800.72  for  20  da.  $  720.18  for  10  da.  8  6282.40  for  15  da. 
$  1200.64  for  15  da.  $  440.70  for  40  da.  f  1460. 84  for  65  da. 
f  8400.60  for  10  da.     $  479.64  for  50  da.       $  1385. 62  for  55  da. 

4.  Find  the  total  amount  of  interest  at  6%  on  : 

$  1800.40  for  90  da.  $  7500.00  for  55  da.  $  216.90  for  20  da. 

$  9200.50  for  80  da.  $  8200.00  for  75  da.  1 432.65  for  15  da. 

$  3240.64  for  70  da.  $  6400.00  for  45  da.  $  832.30  for  10  da. 

$4125.18  for  45  da.  $  1200.45  for  30  da.  $  926.17  for  20  da. 

ORAL  EXERCISE 

1.  What  is  the  interest  on  i  215  for  6  da.  at  6  %  ?  on  $  345  ? 
on  1415?  on  1827.50?  on  $425.90?  on  $4520.60?  State  a 
simple  way  to  find  the  interest  on  any  principal  for  6  da. 
at  6%. 

2.  What  part  of  6  da.  is  3  da.  ?  is  2  da.  ?  is  1  da.  ?  What  is 
the  interest  on  $720  for  6  da.?  for  3  da.  ?  for  2  da.  ?  for  1  da.  ? 
State  a  brief  method  of  finding  the  interest  on  any  principal 
for  3  da.  at  6%;  for  2  da.;  for  1  da. 

3.  Read  aloud  the  following,  supplying  the  missing  words : 
a,    6  da.  minus  ^  of  itself  equals  5  da. ;  6  da.  minus of 

itself  equals  4  da. 

h.   6  da.  plus  ^  of  itself  equals  7  da. ;  6  da.  plus of  itself 

equals  8  da. ;  6  da.  plus of  itself  equals  9  da. 

c.  State  a  short  method  of  finding  the  interest  at  6  %  for  4 
da. ;  for  5  da. ;  for  7  da. ;  for  8  da. ;  for  9  da. 

236.  In  the  above  exercise  it  is  clear  that  removing  the 
decimal  point  in  the  principal  three  places  to  the  left  gives  the 
interest  for  6  da,  at  6<fo* 


222  CONCISE   BUSINESS   ARITHMETIC 

237.   Example.    What  is  the  interest  on  $420  for  8  da.  at 
6%? 


$.420 
.140 


Solution.     Removing  the  decimal  point  three  places  to  the  left  gives 
the  interest  for  6  da.,  or  $0.42.     Since  8  da.  is  6  da.  plus  -}  of  itself, 
$0.42  increased  by  ^  of  itself,  or  $0.56  is  the  required  interest.     In  the      $.5t) 
following  exercises   determine  the  separate  interests  mentally  whenever  it  is 
possible  to  do  so. 

WRITTEN  EXERCISE 

1.  Find  the  total  amount  of  interest  at  6  %  on : 

$800  for  6  da.  $720  for  6  da.  $1500  for  6  da. 

$800  for  3  da.  $720  for  7  da.  $1500  for  5  da. 

$800  for  2  da.  $720  for  8  da.  $1500  for  4  da. 

$800  for  Ida.  $720  for  9  da.  $1500  for  9  da. 

2.  Find  the  total  amount  of  interest  at  6  %  on  : 

$1168  for  6  da.  $1600  for  6  da.  $2400  for  6  da. 

$1168  for  3  da.  $1600  for  7  da.  $2400  for  5  da. 

$1168  for  2  da.  $1600  for  8  da.  $2400  for  4  da. 

$1168  for  1  da.  $1600  for  9  da.  $2400  for  8  da. 

3.  Find  the  total  amount  of  interest  at  6  %  on  : 

$640.50  for  8  da.  $800.10  for  7  da.  $213.80  for  50  da. 

$920.10  for  20  da.  $240.80  for  90  da.  $310.40  for  40  da. 

$280.40  for  15  da.  $960.70  for  70  da.  $135.90  for  10  da. 

$390.60  for  50  da.  $845.60  for  90  da.  $736.18  for  10  da. 

ORAL    EXERCISE 

1.  600  da.  is  how  many  times  60  da.?  If  the  interest  on  $1 
for  60  da.  at  6  %  is  $0.01,  what  is  the  interest  for  600  da.? 

2.  Give  a  rapid  method  for  finding  0.1  of  a  number.  What 
is  the  interest  on  $  500  for  600  da.  at  6  %  ?  on  $  350  ?  on  $  214. 60  ? 
on  $359.80?  on  $4500?  on  $9243.80?  on  $750?  on  $2150? 

3.  What  part  of  600  da.  is  300  da.  ?  200  da.  ?  150  da.  ? 
75  da.  ?   120  da.  ?   100  da.  ?   50  da.  ? 

4.  What  is  the  interest  on  $1400  for  600  da.  ?  for  300  da.  ? 
for  200  da.  ?  for  150  da.  ?  for  75  da.  ?  for  120  da.  ?  for  100 
da.  ?  for  50  da.  ? 


INTEREST  223 

5.  State  a  brief  method  of  finding  the  interest  for  600  da. 
at  6%  ;  for  300  da.  ;  for  200  da. ;  for  75  da. ;  for  50  da.' ;  for 
150  da.  ;  for  100  da. 

6.  If  the  interest  on  f  1  for  600  da.  is  10.10,  what  is  the  inter- 
est for  6000  da.  ?  In  how  many  days  will  any  principal  double 
itself  at  6  %  interest  ? 

7.  What  is  the  interest  on  $1  for  6000  da.  at  6  %  ?  on  $55  ? 
on  $75.60?  on  $18.90?  on  $350?  on  $725?  on  $9125.70. 

8.  What  is  the  interest  on  each  of  the  amounts  in  problem 
7  for  3000  da.  ?  for  2000  da.  ?  for  1000  da  ?  for  1500  da.  ? 

9.  What  is  the  interest  on  $2500  for  6000  da.?  on  $2150  ? 
on  $7500?  on  $790?  on  $155.60? 

10.  What  is  the  interest  on  each  of  the  amounts  in  problem 
9  for  6  da.  ?  for  60  da.  ?  for  600  da? 

238.  In  the  above  exercise  it  is  clear  that  removing  the  deci- 
mal point  in  the  principal  one  place  to  the  left  gives  the  interest 
for  600  da.  at  6(^o  >  ol^o  that  any  sum  of  money  will  double  itself 
in  6000  da.  at  6%. 

WRITTEN  EXERCISE 

Find  the  interest  at  6(fo  on  : 

1.  $240  for  3000  da.  5.  $7420.50  for  600  da.   9.  $1640  for  150  da. 

2.  $318  for  6000  da.  6.  $67218.90  for  30  da.  10.  $1260. 60  for  Ida. 

3.  $912  for  2000  da.  7.  $8400.50  for  400  da.  11.  $17890  for  10  da. 

4.  $316  for  1500  da.  a  $7500.79for  1500da.l2.  $1696  for  100  da. 

ORAL  EXERCISE 

1.  How  many  times  is  6  da.  contained  in  18  da.  ?  in  24  da.  ? 
in  36  da.  ?  in  42  da.  ?  in  54  da.  ?  in  48  da.  ? 

2.  What  is  the  interest  on  $150  for  6  da.  ?  for  18  da.  ?  for 
48  da.  ?  for  54  da.  ?  for  36  da.  ?  for  42  da.  ?  for  12  da.  ? 

3.  What  is  the  interest  on  $350  for  60  da.  ?  for  180  da.  ? 
for  240  da.  ?  for  360  da.  ?  for  420  da.  ?  for  480  da.  ? 

239.  Example.     Find  the  interest  on  $375  for  48  da.  at  6  %. 

SoLDTioy.  37  J  J?  equals  the  interest  for  6  da.  48  da.  is  8  times  *^^'^^^ 
6  da.     Therefore,  the  interest  for  48  da.  is  8  times  37^;*,  or  $3.  $3,000 


224  CONCISE    BUSINESS   AKITHMETIC 

WRITTEN   EXERCISE 

1.  Find  the  total  amount  of  interest  at  6  %  on: 

$750  for  6  da.  1750  for  36  da.  ^750  for  60  da. 

1750  for  12  da.  t750  for  42  da.  $750  for  180  da. 

$750  for  18  da.  $750  for  48  da.  $750  for  240  da. 

2.  Find  the  total  amount  of  interest  at  6%  on: 

$725  for  18  da.  $690  for  6  da.  $450  for  540  da. 

$824  for  36  da.  $129  for  60  da.  $727  for  180  da. 

$729  for  42  da.  $475  for  600  da.  $286  for  240  da. 

$850  for  54  da.  $8600  for  54  da.  $429  for  420  da. 

3.  Find  the  total  amount  of  interest  at  6  %  on: 
$317.40  for  240  da.    $217.18  for  18  da.      $360.40  for  24  da. 
$218.60  for  180  da.    $420.50  for  24  da.      $860.50  for  48  da. 
$419.80  for  420  da.    $240.70  for  540  da.    $900.60  for  66  da. 
$425.60  for  120  da.    $290.60  for  180  da.    $400.80  for  84  da. 

240.  In  some  cases  it  is  advisable  to  find  the  interest  on  the 
principal  for  1  da.  and  then  multiply  by  the  number  of  days. 

ORAL  EXERCISE 

1.  What  is  the  interest  on  $600  for  17  da.  at  6  %  ? 

Solution.     The  interest  for  one  day  is  .000^  of  the  principal,  or  10^.    The 
interest  for  17  da.  is  17  times  10  f,  or  $1.70. 

2.  What  is  the  interest  on  $6000  for  49  da.  at  6^?  on  $300? 
on $240?  on  $3000?  on  $1800?  on  $840?  on  $600? 

3.  State  the  interest  at  6^  on: 

a.  $600  for  19  da.  e,  $6000  for  37  da.  L  $   900  for    17  da. 

b.  $300  for  37  da.  /.  $3000  for  43  da.  J.  $1500  for    40  da. 

c.  $240  for  43  da.  ^.  $2400  for  67  da.  L  $  600  for  139  da. 

d.  $180  for  27  da.  h,  $1800  for  89  da.  L  $  300  for  179  da. 

241.  Frequently  it  is  well  to  mentally  divide  the  days  into 

convenient  parts  of  6  or  60. 

Thus,  97  da.  =  60  da.  +  30  da.  +  6  da.  +  1  da.;  71  da.  =  60  da.  +  10  da. 
+  1  da. ;  49  da.  =  8  times  6  da.  +  1  da. 


7. 

7  da. 

13. 

86  da. 

19. 

17  da. 

8. 

22  da. 

14. 

55  da. 

20. 

25  da. 

9. 

11  da. 

15. 

84  da. 

21. 

85  da. 

10. 

63  da. 

16. 

14  da. 

22. 

89  da. 

11. 

37  da. 

17. 

97  da. 

23. 

19  da. 

12. 

23  da. 

18. 

99  da. 

24. 

29  da. 

INTEREST  225 

ORAL  EXERCISE 

Separate  the  days  in  the  following  exercise  into  6  da.  or  60  da., 
or  into  convenient  parts  of  6  da.  or  60  da. 

1.  8  da. 

2.  67  da. 

3.  27  da. 

4.  13  da. 

5.  72  da. 

6.  43  da. 

242.    Examples,     l.    Find  llie  interest  on  $840  for  31  da.  at 
6%. 

SoLUTiox.    31  da.  =  30  da.  +  1  da.     The  interest  for  CO  da.   is  '^ 

$8.40  and  for  30  da.  ^  of  this  sum  or  $4.20.     The  interest  for  6  da.  is  $4.20 
$0.84  and  for  1  da.  |  of  this  sum  or  $0.14.     Adding  $4.20  and  $0.14  .14 

the  result  is  the  required  interest,  or  $4.34.  S4~34 

2.    What  is  the  interest  on  $2500  for  121  da.  at  6  %  ? 

Solution.     121  da.  =  2  x  60  da.  +  1  da.     The  interest  for  60  da.  ^^^-^Q 

is  $25  and  for  120  da.  twice  this  sum,  or  $50.     The  interest  for  6  $50.00 

da.  is  $2.50  and  for  1  da.  a  of  this  sum,  or  $0.42.     Adding  $50  and  42 

$0.42  the  result  is  §50.42,  the  required  interest.  ^rr^   .^^ 

WRITTEN  EXERCISE 


Find  the  interest : 

Principal 

Time 

Rate 

Principal 

Time 

Rate 

1.    $420 

3  mo. 

6% 

11. 

$450 

4  mo. 

H% 

2.    $650 

4  mo. 

5% 

12. 

$600 

2  mo. 

6% 

3.   $360 

92  da. 

4% 

13. 

$720 

8  mo. 

8% 

4.    $250 

30  da. 

3% 

14. 

$840 

2  mo. 

Hfo 

5.    $380 

24  da. 

7% 

15. 

$120 

7  mo. 

6% 

6.    $900 

55  da. 

6% 

16. 

$280 

9  mo. 

H% 

7.    $550 

47  da. 

3% 

17. 

$885.90 

20  da. 

3% 

8.    $800 

29  da. 

5% 

18. 

.  $240.00 

21  da. 

6% 

9.    $400 

90  da. 

4% 

19. 

$420.18 

25  da. 

n% 

10.    $270 

11  da. 

1% 

20. 

$560.17 

27  da. 

6% 

226  CONCISE   BUSINESS   ARITHMETIC 

243.  It  has  been  observed  that  6  times  $800  =  800  times  $6 ; 
that  0.01  of  1715  =  715  times  10.01 ;  etc.     Hence, 

244.  The  principal  in  dollars  and  the  time  in  days  may  he 
interchanged  without  affecting  the  amount  of  interest. 

245.  Example.    Find  the  interest  on  $600  for  179  da.  at  6  %. 

Solution.   |600  for  179  da.  =  $179  for  600  da.  ;  ^  of  the  principal  equals 
the  interest  for  600  da.  \  ^  ol^  179  =  f  17.90,  the  required  interest. 


$360  for  91  da. 
$420  for  87  da. 
$540  for  21  da. 
$660  for  37  da. 
$750  for  56  da. 
$3600  for  218  da. 
$2000  for  183  da. 
$1200  for  155  da. 
$1800  for  181  da. 
$2400  for  218  da. 


of  itself)  on  interest  for  24  da.  at  6  %,  or  $1500  on  interest  for 
32  da.  (24  da.  +  J  of  itself)  at  6  %.     Hence, 

247.  If  either  the  principal  or  the  time  is  increased  or  decreased 
hy  any  fraction  of  itself  the  interest  is  increased  or  decreased  by 
the  same  fraction. 

248.  Examples,  l.  Find  the  interest  on  $  480  for  279  da. 
at  71  %. 

Solution.  7|  %  is  ^  more  than  6  %.  Increase  the  principal  by  \  of  itself,  and 
the  result  is  $600.  Interchanging  dollars  and  days,  the  problem  is  "Find  the 
interest  on  $279  for  600  da."  Pointing  off  one  place  in  the  new  principal,  the 
result  is  $27.90,  the  required  interest. 

2.    Find  the  interest  on  $2795.84  for  80  da.  at  41%. 

Solution.  4|%  is  {  less  than  6%  interest.  80  da.  decreased  by  \  of  itself 
equals  60  da.    The  interest  on  $2795.84  for  60  da.  =  $27.96,  the  required  result. 


ORAL 

EXERCISE 

State  the  interest  at  6  %  on : 

1.    $60  for  27  da. 

11. 

2.    $30  for  13  da. 

12. 

3.    $20  for  171  da. 

13. 

4.    $10  for  186  da. 

14. 

5.    $15  for  145  da. 

15. 

6.    $12  for  179  da. 

16. 

7.    $10  for  131  da. 

17. 

8.    $100  for  120  da. 

18. 

9.    $200  for  189  da. 

19. 

10.    $150  for  192  da. 

20. 

246.    $1500  on  interest  for  24"  da.  at 

INTEREST  227 

ORAL  EXERCISE 

State  the  interest  on  : 

1.  $279.86  for  45  da.  at  4  %.  6.    12400  for  39  da.  at  5  %. 

2.  $478.65  for  45  da.  at  4%.  7.    12700  for  37  da.  at  4  %. 

3.  $769.64for  48  da.  at  71  %.  8.    $2400  for  87  da.  at  41  %. 

4.  $217.49  for  80  da.  at  41  %.  9.    $1600  for  95  da.  at  41  %. 

5.  $767.53  for  80  da.  at  41  %.  lo. .  $3200  for  59  da.  at  ^  %. 

The  Six  Per  Cent  Method 

249.  This  method  is  best  adapted  to  finding  the  interest 
when  the  time  is  one  year^  or  more  than  one  year, 

ORAL  EXERCISE 

1.  If  the  interest  on  $1  for  1  yr.  at  6  %  is  $0.06,  what  is  the 
interest  on  $  1  for  2  yr.  ?  for  3  yr.  ?  for  4  yr.  ?  for  6  yr.  ?  for 
8  yr.  ?  for  10  yr.  ? 

2.  If  the  interest  on  $1  for  1  yr.  at  6%  is  $0.06,  what  is  the 
interest  on  $1  for  1  mo.?  for  2  mo.  ?  for  3  mo.  ?  for  6  mo.? 
for  10  mo.  ?  for  7  mo.  ?  for  8  mo.  ? 

3.  What  is  the  interest  on  $1  for  1  yr.  6  mo.  at  6%?  for 
2  yr.  6  mo.  ?  for  3  yr.  4  mo.  ?  for  3  yr.  6  mo.  ?  for  4  yr.  8 
mo.  ?  for  1  yr.  10  mo.  ?  for  5  yr.  6  mo.  ?  for  2  yr.  9  mo.  ? 

4.  What  is  the  interest  on  $50  for  1  yr.  at  6  %  ?  for  1  jt. 
6  mo.  ?  for  2  yr.  ?  for  3  yr.  6  mo.  ?  for  2  yr.  8  mo.  ?  for  1  yr. 
10  mo.  ?  for  2  yr.  6  mo.  ?  for  4  yr.  6  mo.  ?  for  1  yr.  9  mo.  ? 

5.  If  the  interest  on  $1  for  1  mo.  at  6  %  is  $0,005  (5  mills), 
what  is  the  interest  for  1  da.  ?  for  2  da.  ?  for  3  da.  ?  for  4  da.  ? 
for  6  da.  ?  for  12  da.  ?  for  18  da.  ?  for  28  da.  ?  for  24  da.  ? 

6.  What  is  the  interest  on  $1  for  1  yr.  1  mo.  1  da.  at  6% ? 
for  2  yr.  3  mo.  3  da.  ?  for  1  yr.  10  mo.  6  da.  ?  for  4  yr.  4  mo. 
24  da.  ?  for  1  yr.  5  mo.  12  da.  ?  for  2  yr.  1  mo.  1  da.  ? 

250.  In  the  above  exercise  it  is  clear  that : 

$0.06  =  interest  on^l  for  1  yr.  at^%. 
$0,005  =  interest  on  $lforl  mo,  at  6  %. 
$0.0001  =  interest  on  $lforl  da,  at  6 %. 


228  CONCISE   BUSINESS   AEITHMETIC 

ORAL  EXERCISE 
Find  the  interest  on  $1  at  6  (Jo  for: 

1.  1  yr.  4  mo.  12  da.  5.    2  yr.  6  mo.  6  da. 

2.  1  yr.  8  mo.  18  da.  6.    3  yr.  4  mo.  9  da. 

3.  1  yr.  7  mo.  24  da.  7.   5  yr.  3  mo.  3  da. 

4.  1  yr.  9  mo.  27  da.  8.   4  yr.  8  mo.  4  da. 
Find  the  interest  at  6%  on: 

9.   $250  for  2  yr.  i4.   8350  for  3  yr. 

10.  $400  for  5  yr.  15.    $450  for  2  yr.  3  mo. 

11.  $700  for  4  yr.  16.   $150  for  1  yr.  6  mo. 

12.  $300  for  3  yr.  4  mo.  17.   $50  for  1  yr.  2  mo.  6  da. 

13.  $500  for  4  yr.  2  mo.  18.   $10  for  2  yr.  6  mo.  6  da. 
251.   Example.    What  is  the  interest  on  $600  for  2  yr.  8  mo. 

15  da.  at  6  %  ? 

Solution.    Find  the    $0.12        =  int.  on  $1  for  2  yr. 
interest  on  $1  for2  yr.;  q^        ^   -^^^  ^^  ^^  ^^^  g  ^^^ 

on  |1   for  8  mo.;    on  ^^^r  •  ^n-i    «•       w       i 

$1  for  15  da.    The  sum  '^^^^  =  1"^.  on  $1  for  15  da. 

of  these  interest  items    $0.1625  =  int.  on  $1  for  the  given  time, 
equals  $0.1625,  the  in-  600  X  $0.1625  =  $97.50,  int.  on  $600 

terest  on    ^1  Jor   the  ^^^  ^  yr.  8  mo.  15  da.  at  6  %. 

given  time  ate %.    Mul-  "^  ' 

tiplying  this  interest  by  the  given  number  of  dollars,  600,  the  product  is  the 
required  interest,  $97.50. 

Sometimes  it  is  shorter  to  find  the  interest  on  $  1  for  the  given  time  at 
any  given  rate,  and  multiply  by  the  number  of  dollars  in  the  principal. 
Thus  to  find  the  interest  on  $400  for  2  yr.  0  mo.  at  8%,  take  400  times  2{)^ 
(2^  X  8^)  ;  on  $500  for  5  yr.  3  mo.  at  4%,  take  500  times  21;^  (5J  x  8^)  ; 
on  $600  for  1  yr.  0  mo.  at  4%  take  000  times  7 ti  etc. 


ORAL  EXERCISE 

Find  the  interest: 

Principal 

Time 

Rate 

Principal 

TnMtE 

Rate 

1.   $400 

1  yr.  2  mo. 

6% 

7.   $840 

1  yr.  6  mo. 

6% 

2.   $500 

2  yr.  4  mo. 

6% 

8.    $100 

3  yr.  6  mo. 

bfo 

3.   $300 

4  yr.  6  mo. 

6% 

9.   $960 

4  yr.  2  mo. 

6% 

4.   $250 

1  yr.  8  mo. 

6% 

10.   $300 

3  yr.  4  mo. 

8% 

5.   $200 

2  yr.  10  mo. 

3% 

11.  $240 

2  yr.  6  mo. 

4% 

6.   $300 

1  yr.  11  mo. 

6% 

12.   $180 

1  yr.  8  mo. 

6% 

INTEREST  229 

WRITTEN  EXERCISE 

Find  the  interest : 

1.  Principal,  $74.90;  time,  6  mo.  15  da. ;  rate,  4  %. 

2.  Principal,  $986.00;  time,  11  mo.  28  da.;  rate,  41%. 

3.  Principal,  11900.00;  time,  10  mo.  28  da.;  rate,  6%. 

4.  Principal,  $87.55;  time,  4  yr.  5  mo.  6  da.;  rate,  6%. 

5.  Principal,  $735.00;  time,  4  yr.  4  mo.  4  da.;  rate,  6%. 

6.  Principal,  $609.50;  time,  2  yr.  7  mo.  6  da.;  rate,  6%. 

7.  Principal,  $875.40;  time,  1  yr.  2  mo.  21  da.;  rate,  4^%. 

8.  Principal,  $1124.75;  time,  1  yr.  5  mo.  14  da.;  rate,  6%. 

9.  Principal,  $1245.00  ;  time,  3  yr.  6  mo.  23  da.;  rate,  6%. 
10.  Principal,  $1570.00;  time,  1  yr.  9  mo.  25  da.;  rate,  5%. 


CHAPTER  XIX 

BANK  DISCOUNT 
ORAL    EXERCISE 

1.  What  is  meant  by  a  promissory  note  ?  by  the  face  of  a 
note  ?    by  the  time  ?    by  the  maker  ?    by  the  payee  ? 

2.  How  would  you  word  a  promissory  note  for  S600,  dated 
at  your  place  to-day,  payable  in  60  da.  at  a  bank  in  your  place, 
with  interest  at  5%,  to  C.  B.  Powell,  signed  by  yourself? 

3.  What  is  meant  by  negotiable  ?  by  indorsing  a  note  ? 
Illustrate  a  blank  indorsement ;  an  indorsement  in  full ;  a 
qualified   indorsement. 

252.  A  commercial  bank  is  an  institution  chartered  by  law  to 
receive  and  loan  money,  to  facilitate  the  transmission  of  money 
and  the  collection  of  negotiable  paper,  and,  in  some  cases,  to 
furnish  a  circulating  medium. 

253.  If  the  holder  (owner)  of  a  promissory  note  wishes  to 
use  the  money  promised  before  it  becomes  due,  a  commercial 
bank  will  usually  buy  the  note,  provided  the  holder  can  show 
that  it  will  be  paid  at  maturity,  that  is,  when  it  becomes  due. 
This  is  called  discounting  the  note. 


230 


BANK   DISCOUNT  231 

254.  A  commercial  draft  is  now  frequently  used  instead  of 
the  promissory  note  as  security  for  the  payment  of  goods  sold 
on  credit.  Such  a  draft  may  be  defined  as  a  written  order  in 
which  one  person  directs  another  to  pay  a  specified  sum  of 
money  to  the  order  of  himself  or  to  a  third  person. 

The  circumstances  under  which  the  foregoing  draft  was  drawn  are  as 
follows  :  Geo.  H.  Catchpole  sold  Frank  G.  Hill  goods  amounting  to  ^460.80. 
Terms :  30-da.  draft.  The  draft  and  an  invoice  were  made  out  and  sent 
to  Frank  G.  Hill  by  mail.  Frank  G.  Hill  accepted  the  draft,  that  is,  signi- 
fied his  intention  to  pay  it  by  writing  the  word  accepted^  the  date,  and  his 
name  across  the  face.  The  draft  was  then  returned  to  Geo.  H.  Catchpole, 
who  may  discount  it  the  same  as  he  would  an  ordinary  promissory  note. 

The  parties  to  a  draft  are  the  drawer,  the  drawee,  and  the  payee.  In  the 
foregoing  draft  Geo.  H.  Catchpole  is  both  the  drawer  and  the  payee,  and 
Frank  G.  Hill  is  the  drawee. 

A  draft  payable  after  sight  begins  to  mature  from  the  date  on  which  it 
is  accepted.  An  acceptance  must,  therefore,  be  dated  in  a  draft  payable 
after  sight,  but  it  may  or  may  not  be  dated  in  a  draft  payable  after  date. 

SBu/faio.  jr.y., (^^^^k^^.  ^, f9 — 


^^/^^^ 


'^  y^^^-v!^^..^^^^  "^y/^t ^:=^Q)oUara 


to  tieeount  of 


'3^ 


^z^^^Z^^*^ 


^ 


\~r<;6f^^^^y^^r^^J^^^^^^ 


Some  states  allow  three  days  of  grace  for  the  payment  of  notes  and  other 
negotiable  paper.  Days  of  grace  are  obsolete  in  so  many  of  the  states  that 
they  are  not  considered  in  the  exercises  in  this  book.  Some  states  provide 
that  when  paper  matures  on  Sunday  or  a  legal  holiday  it  must  be  paid  the 
day  preceding  such  Sunday  or  legal  holiday ;  others  provide  that  it  must  be 
paid  on  the  day  following.  To  hold  all  interested  parties,  the  laws  of  any 
given  state  should  always  be  observed.  When  the  time  of  negotiable  paper 
is  expressed  in  months,  calendar  months  are  used  to  determine  the  date  of 
maturity ;  but  when  the  time  is  expressed  in  days,  the  exact  number  of  days 
is  used.  Thus,  a  note  payable  2  mo.  after  July  15  is  due  Sept.  15 ;  but  a 
note  payable  60  da.  after  July  15  is  due  Sept.  13.  Paper  payable  1  mo. 
from  May  31,  Aug.  31,  etc.,  is  due  June  30,  Sept.  30,  etc. 


232 


CONCISE   BUSINESS   ARITHMETIC 


255.  The  time  from  the  date  of  discount  to  the  maturity  of 
paper  is  called  the  term  of  discount ;  the  whole  sum  specified  to 
be  paid  at  maturity,  the  value,  or  amount,  of  the  paper. 

The  term  of  discount  is  usually  the  exact  number  of  days  from  the  date  of 
discount  to  the  date  of  maturity.  Some  banks,  however,  find  the  term  of 
discount  by  compound  subtraction,  and  then  reduce  the  time  to  days ;  e.g. 
the  term  of  discount  on  a  note  due  May  6  and  discounted  Mar.  1  is  counted 
as  2  mo.  5  da.,  or  65  da.  In  this  text  the  term  of  discount  is  the  exact  number 
of  days  from  the  date  of  discount  to  the  maturity  of  the  paper. 

256.  The  reduction  made  by  a  bank  for  advancing  money  on 
negotiable  paper  not  due  is  called  bank         m* 

discount.  The  value  of  negotiable  paper 
at  maturity,  minus  the  bank  discount,  is 
called  the  proceeds. 

Bank  discount  is  always  the  simple  interest  for 
the  term  of  discount  on  the  whole  sum  specified  to 
be  paid  at  maturity. 

257.  The  accompanying  maturity  table 
is  sometimes  used  by  bankers  in  finding 
the  maturity  of  notes  and  drafts.  The 
following  examples  illustrate  its  use. 

258.  Examples,  l.  Find  the  maturity 
of  a  note  payable  (a)  6  mo.  from  Apr.  27, 
1915;  (5)  6  mo.  from  Sept.  25,  1915. 

Solutions,  (a)  Refen-ing  to  the  table,  observe 
that  April  is  the  4th  month;  adding  4  and  6,  the 
result  is  10,  and  the  10th  month  (see  number  on  left) 
is  October.    The  note  is  therefore  due  Oct.  27,  1915. 

(6)  September  is  the  9th  month.  9  +  0  =  15,  and  the  15th  month  (see  number 
on  right)  is  March  of  the  next  year.     The  note  is  therefore  due  Mar.  25,  1916. 

2.    Find  the  maturity  of  a  note  payable  90  da.  from  Jan.  18, 

1916. 

Solution.  1  +  3  =  4,  and  the  4th  month  is  April.  If  the  note  were  pay- 
able in  3  mo.,  it  would  be  due  Apr.  18.  Referring  to  the  table,  note  that  2 
da.  (1  da.  +  1  da.)  must  be  subtracted  for  January  and  March,  and  2  da.  added 
for  February.     The  note  is  therefore  due  Apr.  18. 

After  the  student  has  become  familiar  with  the  principles  of  the  table  it  will 
not  be  found  necessary  to  consult  it. 


1 

Jan.  -  1 

13 

2 

Feb.  +  2 

14 

3 

Mar.  -  1 

15 
16 

4 

Apr. 

5 
6 

May-1 

17 
18 
19 

June 

7 

July  -  1 

8 

Aug.  -  1 

20 
21 
22 

9 

Sept. 

10 

Oct.  -  1 

11 

Nov. 

23 

12 

Dec.  -  1 

24 

BANK   DISCOUKT 


233 


ORAL   EXERCISE 
Find  the  maturity  of  each  of  the  following  notes : 
Date  Time 

1.  Apr.  6,  1915  30  da. 

2.  Oct.  6,  1916  3  mo. 

3.  Nov.  9,  1915  60  da. 

4.  Jan.  31,  1916  1  mo. 

5.  Sept.  18,  1915  90  da. 

Find  the  maturity  of  each  of  the  following  acceptances  : 

Datf-  ^'^®  AFTER  J.  Time  after 

^^^^  Date  ^^^^  Date 

11.  Apr.  3  30  da.  14.    Dec.  31  2  mo. 

12.  May  5  60  da.  15.    Jan.  12 

13.  Jan.  20  1  mo.  16.    Feb.  18 
Find  the  maturity  of  each  of  the  following  acceptances 


Date 

6.  Jan.  30,  1916 

7.  Jan.  31,  1915 

8.  May  10,  1916 

9.  June  19,  1916 
10.   Nov.  15,  1916 


Time 
30  da. 
30  da. 
90  da. 
60  da. 
30  da. 


1  mo. 

3  mo. 


17. 
18. 
19. 


Date 
Accepted 

Aug.  12 
Sept.  18 
Oct.   30 


Time  after 
Sight 

3  mo. 
2  mo. 

4  mo. 


20. 
21. 
22. 


Date 
Accepted 

Apr.  25 
May  17 
June  18 


Time  after 
Sight 

60  da. 

3  mo. 

30  da. 


WRITTEN   EXERCISE 

Find  the  maturity  and  the   term  of  discount 
Date 

1.  Jan.   16,  1916 

2.  Jan.   31,  1916 

3.  Feb.  12,  1916 

4.  Feb.  24,  1916 

5.  Mar.  31,  1916 

Date  of  Draft        Time  after  Date 

6.  Feb.  7  60  da. 

7.  Mar.  12  30  da. 
Date  of  Draft  Time  after  Sight 

8.  May  31  60  da. 

9.  Mar.  17  90  da. 


Time 

Discounted 

3  mo. 

Mar.  1 

1  mo. 

Feb.  3 

90  da. 

Mar.  2 

60  da. 

Apr.  1 

90  da. 

May  13 

Date  Accepted 

Date  Discounted 

Feb.    8 

Feb.    9 

Mar.   12 

Mar.  15 

Date  Accepted 

Date  Discounted 

May  31 

June  3 

Mar.  20 

Mar.  21 

234 


CONCISE   BUSINESS   ARITHMETIC 


259.    The  following  time  table  is  frequently  used  by  bankers 
in  finding  the  exact  number  of  days  between  any  two  dates  : 


Table  of  Time 


From  Any 

Day 

To  THE  Same  Day  of  the  Next 

OF 

Jan. 

Feb. 
31 

Mar. 
59 

Apr. 

90 

May 
120 

Jane 
151 

July 
181 

Aug. 
212 

Sept. 

Oct. 

Nov. 

Dec. 

January  .... 

365 

243 

273 

304 

334 

Febkuary 

334 

365 

28 

59 

89 

120 

150 

181 

212 

242 

273 

303 

March   . 

306 

337 

365 

31 

61 

92 

122 

153 

184 

214 

245 

275 

April  .  . 

275 

306 

334 

365 

30 

61 

91 

122 

153 

183 

214 

244 

May  .  . 

245 

276 

304 

335 

365 

31 

61 

92 

123 

153 

184 

214 

June  .  .  . 

214 

245 

273 

304 

334 

365 

30 

61 

92 

122 

153 

183 

July  .  . 

184 

215 

243 

274 

304 

335 

365 

31 

62 

92 

123 

153 

August  . 

153 

184 

212 

243 

273 

304 

334 

365 

31 

61 

92 

122 

September 

122 

153 

181 

212 

242 

273 

303 

334 

365 

30 

61 

91 

October  . 

92 

123 

151 

182 

212 

243 

273 

304 

335 

365 

31 

61 

November 

61 

92 

120 

151 

181 

212 

242 

273 

304 

334 

365 

30 

December 

31 

62 

90 

121 

151 

182 

212 

243 

274 

304 

335 

365 

The  exact  number  of  days  from  any  day  of  any  month  to  the  correspond- 
ing day  of  any  other  month,  within  a  year,  is  found  in  the  column  of  the 
last  month  directly  opposite  the  line  of  the  first  month.  Thus,  from  June 
6  to  Sept.  6  is  92  da. ;  from  Apr.  1  to  Oct.  1  is  183  da. ;  from  Aug.  26  to 
Dec.  26  is  122  da.  The  exact  number  of  days  between  any  two  dateSj  leap 
years  excepted,  is  found  as  in  the  following  illustrations : 

260.    Examples,    l.    How  many  days  from  Mar.  1  to  May  11? 

Solution.  From  Mar.  1  to  May  1  is  61  da.  From  May  1  to  May  11  is  10 
da.     61  da.  +  10  da.  =  71  da.,  the  required  result. 

2.    How  many  days  from  July  26  to  Oct.  6  ? 

Solution.  From  July  26  to  Oct.  26  is  92  da.  From  Oct.  26  back  to  Oct.  6 
is  20  da.     92  da.  —  20  da.  =  72  da.,  the  required  result. 


ORAL  EXERCISE 


Bt/  the  table  find  the  exact  number  of  days  from : 


1.  July  8  to  Sept.  8. 

2.  Jan.  6  to  Mar.  6. 

3.  Jan.  23  to  June  23. 

4.  Feb.  13  to  July  13. 

5.  Mar.  11  to  Sept.  11. 

6.  Mar.  21  to  Aug.  21. 


7.  May  31  to  Aug.  1. 

8.  Feb.  23  to  Sept.  23. 

9.  Mar.  24  to  July  12. 

10.  May  11  to  Aug.  31. 

11.  Aug.  15  to  Dec.  10. 

12.  Nov.  25  to  Mar.  25. 


BANK   DISCOUNT 


235 


261.  Examples,     l.    Find  the  proceeds  of  a  note  for  S3000, 

payable  in  78  da.,  discounted  at  6  %. 

Solution.     78  da.  =  the  term  of  discount. 
$  39  =  the  bank  discount. 
$3000  —  $39  =  $2961,  the  proceeds. 

2.  A  note  for  S6000,  payable  in  60  da.  from  May  10,  1915, 
with  interest  at  6  %,  is  discounted  May  25,  at  6  %.  Find  the 
maturity,  tlie  term  of  discount,  the  bank  discount,  and  the 
proceeds. 

Solution.     July  9,  1915  =  the  maturity. 

45  da.  =  tlie  term  of  discount. 

$60  =  the  interest  on  the  note  for  60  da. 
$6060  =  tlie  value  of  the  note  at  maturity. 
$45.45  =  the  bank  discount. 
$6014.55  =  the  proceeds. 

262.  The  accompanying  diagram  illustrates  a  convenient 
outline  for  learning  the  proper 
method  of  computing  bank  dis- 
count. It  will  be  observed  that 
the  first  problem  is  an  interest- 
bearing  note,  and  the  second 
problem  a  non-interest-bearing 
note.  The  items  in  black  ink 
are  taken  from  the  problem,  and 
the  items  in  red  ink  are  found 
as  previously  explained. 


^^^<t^y»t-o-^.-a>'»t>e^*g^ 


^<^tUS^<«^ 


/J 

f303 
//.S2. 

<3o. 


■«r  (rfC.fi 


WRITTEN    EXERCISE 

1.  Assuming  that  the  model  draft,  page  252,  was  discounted 
July  20,  at  6%,  find  the  bank  discount  and  the  proceeds. 

2.  Assuming  that  the  model  draft,  page  230,  was  discounted 
May  30,  at  6  %,  find  the  bank  discount  and  the  proceeds. 

3.  Assuming  that  the  model  draft,  page  231,  was  discounted 
April  26,  at  6  %,  find  the  bank  discount  and  the  proceeds. 

4.  Assuming  that  the  model  draft,  page  230,  wa.s  discounted 
May  15,  at  6%,  find  the  bank  discount  and  the  proceeds. 


236  CONCISE   BUSINESS   AKITHMETIC 

5.  Assuming  that  the  model  draft,  page  231,  was  discounted 
April  12,  at  6%,  find  the  bank  discount  and  the  proceeds. 

6.  Find  the  proceeds  of  the  following  joint  note: 
$895.40  Baltimore,  Md.,  May  25,  1915. 

Six  months  after  date,  for  value  received,  we  promise  to  pay- 
to  the  order  of  Ralph  D.  Gibson  Eight  Hundred  Ninety-five 
^Yo  Dollars,  at  Exchange  National  Bank. 

Seth  M.  Bullard. 
Discounted  July  2,  1915,  at  5%.  Isaac  C.  Watkins. 

7.  Find  the  proceeds  of  the  following  joint  and  several  note: 
11000.00  Columbus,  O., May  1,  1915. 

Three  months  after  date  we  jointly  and  severally  promise  to 
pay  to  the  order  of  Wilson  N.  Burton  One  Thousand  Dollars, 
at  Second  National  Bank,  Columbus,  O.,  with  interest  at  6%. 

Value  received.  John  M.  Sellers. 

Discounted  June  2,  1915,  at  G  %.         Daniel  W.  Sheldon. 

8.  Find  the  proceeds  of  the  following  firm  note: 
$1250.00  St.  Louis,  Mo.,  Aug.  20,  1915. 

Ninety  days  after  date  we  promise  to  pay  to  the  order  of 
C.  M.  Courtwright  Twelve  Hundred  Fifty  Dollars,  at  the 
National  Bank  of  Redemption,  with  interest  at  5%. 

Value  received.  J.  M.  Cox  &  Son. 

Discounted  Sept.  1, 1915,  at  6  %. 

9.  Sept.  26  you  sold  R.  M.  Stein,  Portland,  Me.,  a  bill  of 
hardware  amounting  to  ^2480,  less  20  %,  25  %,  and  10  %.  Terms: 
^  by  60-da.  note  with  interest  at  6  %  ;  |-  on  account  60  da.  What 
was  the  amount  of  the  note  which  was  this  day  received? 

10.  Oct.  12  you  discounted  at  Union  Bank,  at  6  %,  R.  M. 
Stein's  note  received  Sept.  26,  the  bank  giving  you  credit  for 
the  proceeds.  If  the  bank  charges  -^-^  %  for  collecting  out-of- 
town  paper,  what  was  the  amount  of  the  proceeds  credited  ? 

A  small  fee  called  collection  and  exchange  is  sometimes  charged  on 
discounted  paper  payable  out  of  town.  The  charge  is  by  no  means 
uniform,  being  controlled  largely  by  the  size  of  the  depositor's  account  and 
the  general  custom  of  the  banks  in  any  given  locality. 


BANK  DISCOUNT 


237 


11.  The  following  is  a  part  of  a  page  from  a  bank's  discount 
register.  Copy  it,  supplying  all  missing  terms.  The  notes 
were  all  discounted  June  17. 


No. 

Date  of 

Time 

When 

Teem  op 

Rate  of 

Value  of 

Disc. 

Coll.  & 

Peoceeds 

Papee 

Dub 

Discount 

Discount 

Papke 

EXCH. 

Ceeditbd 

20 

Apr.  25 

3  mo. 

6  7o 

2000 

00 

21 

May  1 

3  mo. 

6% 

3500 

00 

3 

50 

22 

Apr.  1 

90  da. 

6% 

1500 

00 

23 

Apr.  15 

90  da. 

6% 

900 

60 

24 

June  15 

30  da. 

6% 

378 

90 

38 

12.  Sept.  15  your  balance  in  the  First  National  Bank  was 
$1725.90.  You  immediately  offered  for  discount,  at  6%,  the  fol- 
lowing notes,  the  proceeds  of  which  were  to  be  placed  to  your 
credit :  E.  M.  Robinson's  30-day  note  dated  Sept.  1,  for  S  300 ; 
C.  E.  Reardon's  note  payable  3  mo.  from  July  25,  with  interest 
at  6%,  for  S 427.65;  C.  W.  Allen's  60-day  note  dated  Aug.  1, 
for  $321.17;  F.  H.  Clark's  60-day  note  dated  July  30,  for 
$1500.  What  was  your  credit  at  the  bank  after  discounting  the 
notes  ? 

13.  April  6,  1915,  Peter  W.  Berger  has  on  deposit  in  the 
First  National  Bank  $523.87.  He  draws  a  check  for  $1176.45, 
and  then  discounts  the  following  notes  at  the  bank,  at  6%, 
receiving  credit  for  the  proceeds.  What  was  the  balance  of  his 
account  after  the  notes  were  discounted  and  credited  ? 

a. 
f  346. 50  Hartford,  Conn.,  Mar.  1, 1915. 

Ninety  days  after  date  I  promise  to  pay  Peter  W.  Ber- 
ger, or  order.  Three  Hundred  Forty-six  -^^^  Dollars,  at  First 
National  Bank,  Hartford,  Conn. 

Value  received.  Henry  S.  Lake. 

6. 
$575.00  Hartford,  Conn.,  Feb.  1, 1915. 

Aug.  1,  1915,  I  promise  to  pay  Peter  W.  Berger,  or  order, 
Five  Hundred  Seventy -five  Dollars,  at  Second  National  Bank, 
Hartford,  Conn. 

Value  received.  Samuel  D.  Skiff. 


238 


CONCISE   BUSINESS    ARITHMETIC 


14.  July  18,  C.  B.  Snow's  bank  balance  is  S312.90.  He  dis- 
counts  at  6%  the  following  drafts,  and  then  issues  a  check  in 
payment  for  5  sewing  machines  at  S75,  less  20%  and  25%. 
What  is  the  amount  of  liis  balance  after  issuing  the  check  ? 


a. 


$.im^     ^ 


IMan 


tNio.J^Sl'i 


T^JfrrT;^^ 


/..-^.-fp-r^J-^ 


S^fLGJtrrr 


Rochester,  tNl^Y.,      Jlf^^f /^, /9 

^^<^^^^^!!^.<?-.-^7gz::^?cz^^gfk-  ■^-  -  'Pntj  to  the  order  of 


."Dollar 


Ko.M^T>Ui 


-T^-^g^ 


^^^'tr-r^y 


BANK  LOANS 

263.  The  foregoing  exercises  have  references  to  paper  bought 
or  discounted  by  a  bank.  Money  is  frequently  loaned  upon 
the  notes  of  the  borrower,  indorsed  by  some  one  of  known 
financial  ability,  or  secured  by  the  deposit  of  stocks,  bonds, 
warehouse  receipts,  or  other  collaterals.  These  notes,  if  drawn 
on  time,  are  not  interest-bearing,  but  the  bank  discounts  them 
by  deducting  from  their  face  the  interest  for  the  full  time. 


BANK   DISCOUNT  239 

264.  Loans  are  sometimes  made  on  call  or  demand  notes  ;  that 
is,  on  notes  that  can  be  called  or  demanded  at  any  time  after 
they  are  made.  These  notes  are  interest-bearing  and  are  drawn 
for  the  exact  sum  loaned. 

Call  or  demand  loans  generally  bear  a  lower  rate  of  interest  than  loans 
on  time.  They  are  made  principally  to  brokers  and  investors,  who  use 
them  to  pay  for  stocks  ;  but  they  are  also  made  to  merchants  and  others  to 
some  extent.  Business  men,  however,  generally  prefer  to  borrow  on  time, 
for  they  do  not  wish  to  be  embarrassed  by  having  the  loans  called  in  at  an 
unexpected  time.  Time  loans  are  usually  drawn  for  thirty,  sixty,  or  ninety 
days.  If  the  borrower  requires  money  for  a  longer  period,  the  bank  will 
usually  allow  him  to  renew  the  note  when  it  falls  due. 

WRITTEN    EXERCISE 

1.  Jan.  7,  1915,  E.  L.  Jennings  &  Co.  desire  to  extend  their 
business,  and  for  this  purpose  borrow  money  at  6  %  of  the  First 
National  Bank  of  New  York,  on  the  following  note.  How  much 
will  the  bank  place  to  the  credit  of  E.  L.  Jennings  &  Co.  ? 

^.fTP^^-^  J^ewYorA, Jlr^^^.  /, 79 

■'  /^c^.^?^  ^^Z^^'*:fC'i^^^^ nffff-  date  ^-U^T^  promlae  to  pay  to 

tAe  order  of  ^-X^<^.<£^  X/^,^..-'??^?^.^-7?7,^"7^V^  ~-  "  

-^'^^k^^^n/t^.^^^.d^^^'y^,^ — : g)n//^^ 


at  ^^L:Ji^^^^-T>^.^f7..'^^<i^^  -^^f>-f^.^^y  - 


Value  received 


2.  You  gave  the  Union  National  Bank,  of  your  city,  your 
note  for  S1200,  at  60  da.,  indorsed  by  Williams  &  Rogers. 
How  much  cash  will  the  bank  advance  you  if  discount  is 
deducted  at  the  rate  of  6  %  ? 

3.  Howe  &  Rogers,  Buffalo,  N.  Y.,  borrowed  $12,000  of 
Merchants  National  Bank  on  their  demand  note  secured  by  300 
shares  of  Missouri  Pacific  Railway  stock  at  S50.  If  the  rate 
of  interest  was  2i%,  how  much  was  required  for  settlement 
39  da.  after  the  loan  was  made? 


240  CONCISE   BUSINESS  ARITHMETIC 

4.  Jan.  2,  1915,  C.  W.  Allen  &  Co.,  brokers,  borrowed  of 
First  National  Bank,  Boston,  Mass.,  S  15,000  on  the  following 
collateral  note.  How  much  was  required  for  full  settlement 
of  the  loan  57  da.  after  it  was  made  ? 


$/.f^^/7^ Eoslon,  Mass. , J^^g2>^^^.   Z, / 9 

.,     C  y^^..'t^c.£^^^^^..'i:^.''7^^^ for  value  receioed,  ^-JV^-  prombe  to  pay  to  the  order  of 

r:^i:^^^<^<^/)^.^^^^-t^^^  at  their  banking  home 


-^./-^^ 


As  collateral  security  for  the  payment  of  the  note  and  all  other  liabilities  to  said  bank,  either  absolute  or 
contingent,  now  existing  or  to  be  hereafter  incurred,  -<'</%-  have  deposited  with  it : 

Should  the  market  value  of  the  same  decline,  -Cert-  promise  to  furnish  satisfactory  additional  collateral  on 
demand,  which  may  be  made  by  a  notice  in  writing,  sent  by  mail  or  otherwise,  to  ^P-t^--r-'  residence  or  place  of 
business.  On  the  nonperformance  of  either  of  the  above  promises  -tt/~t^  authorize  the  holder  or  holders 
hereof  to  sell  said  collateral  and  any  collaterals  added  to  or  substituted  for  the  same,  without  notice,  at  public  or 
private  sale,  and  at  or  before  the  maturity  hereof,  he  or  they  giving  -«-'d^  credit  for  any  balance  of  the  net 
proceeds  of  such  sale  remaining  after  paying  all  sums  absolutely  or  contingently  due  and  then  or  thereafter 
payable  from  -^£<^  to  said  holder  or  holders.  And  ~<crt-  authorize  said  holder  or  holders,  or  any  person  iix 
his  or  their  behalf,  to  purchase  at  any  such  sale.  ^^  >-a   /      ^  ^rp»*N 


FINDING  THE  FACE 

265.  Example.  I  wish  to  borrow  $1980  of  a  bank.  For 
what  sum  must  I  issue  a  60-da.  note  to  obtain  the  amount, 
discount  being  at  the  rate  of  6  %  ? 

Solution.  Let  the  face  of  the  note  =  $  1 

Then  the  bank  discount  =  $0.01 
And  the  proceeds  =  $0.99 

But  the  proceeds  -  %  1980 

1 1980 -^$0.99  =    2000 

.-.  the  face  of  the  note  is  2000  x  $1,  or  $2000. 

WRITTEN    EXERCISE 

1.  What  must  be  the  face  of  a  30-da.  note  in  order  that  when 
discounted  at  6%  the  proceeds  will  be  S1990  ?  of  a  60-da.  note, 
same  conditions  ? 

2.  You  wish  to  borrow  S  3940  cash.  What  must  be  the  face 
of  a  90-da.  note  in  order  that  when  discounted  at  6%  the 
proceeds  will  be  the  required  sum  ? 


BAXK  DISCOUNT 


241 


A  WRITTEN  REVIEW  TEST 

(Time,  approximately,  forty  minutes) 

Co]py  each  of  the  following  problems ;  complete  the  worh^  and 
check  the  result. 

When  a  certain  number  of  days  is  written  in  the  Discount  column,  compute 
the  discount  at  6%  for  the  given  time.  When  Jg.%  is  written  in  the  Collection 
and  Exchange  column,  compute  the  collection  on  the  face  of  the  paper. 

When  copying  the  problem  do  not  copy  the  number  of  days  in  the  dis- 
count column,  nor  the  ■^■^%  in  the  collection  and  exchange  column,  but  com- 
pute the  discount  or  the  collection  and  enter  the  result  in  the  required  column. 


Face  of  Paper 

1.  S856.40 
442.50 
365.30 
297.45 
175.40 
217.50 
246.30 


Discount 

S3.56 
2.21 

60  da. 
2.97 
1.75 
2.18 

soda. 


Coll.  &  Exch. 

$0.36 
0.44 
0.37 

0.18 


Proceeds 
? 
? 
? 
? 
? 
? 
? 


? 

? 

? 

? 

Face  of  Paper 

Discount 

Coll.  &  Exch. 

Pkoceuus 

2.  S325.65 

S1.63 

$0.33 

? 

150.60 

90  da. 

0.15 

? 

327.85 

3.28 

0.33 

? 

180.96 

60  da. 

tV% 

? 

313.46 

3.13 

0.31 

? 

286.32 

1.43 

0.29 

? 

? 

? 

? 

? 

Face  of  Paper 

Discount 

Coll.  &  Exch. 

Proceeds 

3.  S422.50 

30  da. 

tV% 

? 

384.20 

S3.84 

$0.38 

? 

519.40 

5.19 

0.52 

? 

280.50 

90  da. 

0.28 

? 

375.90 
245.32 

1.25 
2.45 

? 
? 

.tV% 

CHAPTER  XX 

EXCHANGE 
DOMESTIC   EXCHANGE 

ORAL    EXERCISE 

1.  Mention  some  objections  to  sending  actual  money  by 
express. 

2.  If  S50  sent  by  mail  in  a  registered  letter  is  lost,  to  what 
extent  are  the  postal  authorities  liable  ? 

3.  In  what  ways  may  you  pay  a  debt  at  any  distant  point 
without  actually  sending  the  money? 

266.  The  process  of  settling  accounts  at  distant  points  with- 
out actually  sending  the  money  is  called  exchange. 

Money  Orders 

267.  Money  orders,  as  issued  by  post  offices,  express  com- 
panies, and  banks  are  frequently  used  in  making  payments  at 
a  distance. 

268.  A  postal  money  order  is  a  government  order  for  the 
payment  of  money,  issued  at  one  office  and  payable  at  another. 


61596     Westfield,  Sta.1,Mass. 


3746 


United  States  Postal  Money  Order 


XA 


DOLLARS  /     _^ 

-^yV  CENT. 


PAY  AMOUNT  STATED  ABOVE  TO  ORI 
"        IF  ISSUED  WITHIN  THE  COI 

POSTMASTER 

UNITED  STATES,  ALASKA  EXCEPTED 


OF  PATEE  NAMED 
NENTAL  UNITED  : 


JHIBTmATS  /ROM  DATE  OF  ISai 


RECEIVED  PAYMENT: 

FACSIMILE.  OF  NO  VALUE 


Westfield,  Sta.  1 ,  Mass.  3746 

61596  «:=ii--. 

""  """"    Coupon  for  Paytngr  Office 


J  THIS  MONEY  ORDER  IS  NOT  GOOD 

5  FOR  MORE  THAN  LARGEST  AMOUNT 

I  INDICATED  ON  LEFT-HAND  MARGIN 

Z  OF  THE  ORDER  AND  ANY  ALTERA- 

<  TION  OR  CRAaURE  RENDERS  IT  VOID 


242 


EXCHANGE  243 

The  fees  (rate  of  exchange)  charged  for  postal  money  orders  are : 

For  orders  for  sums 

Not  exceeding  $2.50    Zf  Over  $30.00  to  .$40.00  \hf 

Over  $2.50  to      5.00    hf  Over     40.00  to      50.00  \%f 

Over     5.00  to   10.00    8^  Over     50.00  to      60.00  20)* 

Over  10.00  to   20.00  10^  Over     60.00  to      75.00  25)? 

Over  20.00  to   30.00  VI  f  Over     75.00  to   100.00  Z^f 

The  maximum  amount  for  which  a  single  postal  money  order  may  be 
issued  is  $  100.  When  a  larger  sum  is  to  be  sent,  additional  orders  must 
be  obtained.  When  an  order  is  issued,  the  money  is  not  sent  from  one 
post  office  to  another.  The  transfer  is  merely  a  matter  of  bookkeeping, 
the  money  being  received  by  the  government  at  one  office  and  paid  out 
at  another.  If  a  postal  money  order  is  lost,  a  duplicate  may  be  obtained 
from  the  Post  Office  Department  at  Washington. 

269.  An  express  money  order  is  an  order  for  the  payment 
of  money  issued  by  an  express  company  and  payable  at  any 
of  its  agencies. 

if.mf/;. 
When  G^untersigned 

BYAOENTATPOINT  OF  ISSUE 


Ber  TO  THE  ORDER  llF^^:^^^~;^fe^^^.>.<^;;^^^   at'^^^/^^,...;^^  .  >^^^^^ 
The  Sum  of   /Z^^<i<>^^7^^.^^-^     //cm,  -^ Dollars 


GOOO  FOR  MORC  THAN  THE  HJGMC3T  PRiNTtD  M>MtCJNAL  AHOUHT.    IN  NO  CASE  TO  EXCEED  I 


"""CT^^^^^^^^J/  AecNT  <:::^>c^i^Sr<x_ 


'""i^^^7'-^S^e<;^^^^       State  op  /'/f^^,^^^       name  oi- »EM«»e«  /-"i^-) 

.TE    \le^y  ^/, ,9 ^^Z^r^^^^04^-^^v 

^  /  Axr  ERASURE.ALTCRATION.DEFACEMENTORMUtnATIONOFTHIS  ORDCRRENOERS  rrvOIO.  / 

The  fees  charged  for  express  money  orders  are  the  same  as  those  for 
postal  money  orders.  The  maximum  amount  for  which  a  single  express 
money  order  may  be  issued  is  $50.  A  postal  money  order  must  not  bear 
more  than  one  indorsement,  but  an  express  money  order  may  bear  any 
number  of  indorsements. 

270.  A  bank  money  order  (see  form,  page  244)  is  an  order 
for  the  payment  of  money  issued  by  a  bank  and  payable  at 
certain  other  banks  in  different  parts  of  the  country. 

The  charge  for  a  bank  money  order  is  usually  the  same  as  that  for  a 
postal  money  order. 


244 


CONCISE   BUSINESS   ARITHMETIC 


CAPITAL 


1 


MONEY    ORDER 
NOT    OVER 

Fl  F"TV    DOL-UARS 


Boston  Mas 


The  N 


TO  ANV   BANK    NAMED 
ONTHE    BACKOrTHlS    DRAPT 


ANK 


271.  A  telegraphic  money  order  is  a  telegram  of  an  express 
or  telegraph  company,  at  any  given  place,  ordering  the  pay- 
ment of  money  at  another  designated  place. 

THE  UNION  TELEGRAPH  CO. 


INCORPORATED 


23.000  OFFICES  IN  AMERICA 


CABLE  SERVICE  TO  ALL  THE  WORLD 


ROBERT  C.  CLOWRY,  President  and  General  Manager 


w  t  iM  U  the  following  message  subject 
terms  on  back  hereof,  which  are  hereby  agreed 

"YO       The  Union  Telegraph  Co, 


to  the  \ 
sedto.  ^ 


Boston.   Mass..    July  27, 


19 


Rochester,   N.Y, 


Findahle 
Findelkind 


Charles 


Osgood 


ten 


East 


Avenue 


Fi chant 


The    Union    Telegraph    Co. 


These  telegrams  are  usually  in  cipher ;  that  is,  in  a  language  not  under- 
stood  by  those  who  are  unfamiliar  with   the   system   of   abbreviations 
(code)  used.    The  sender  and  the  receiver  must  each  have  a  code.    The 
following  code  will  illustrate  the  principle  of  telegraphing  in  cipher : 
Code  Word  Meaning 

Fickant  One  hundred  dollars 

Ficheron  One  thousand  dollars 

Findable  Please  pay of your  city  I . 

Findelkind  On  production  by  him  of  positive  evidence 

of  his  personal  identity. 
The  principle  of  a  telegraphic  money  order  is  the  same  as  that  of  a  postal 
money  order;  no  money  is  transferred  from  one  place  to  another.   The 
charge  for  an  order  is  usually  1%  of  the  amount  to  be  transmitted  plus 
twice  the  rate  for  a  single  ten-word  message. 


EXCHANGE  245 

The  following  are  the  rates  for  a  ten-word  message  from  Boston  to  the 
places  named : 

New  York        $0.30  Chicago  -10.50  Galveston     $0.75 

Philadelphia     $0.35  San  Francisco     11.00  Rochester    $0.40 

ORAL  EXERCISE 

1.  What  was  the  total  cost  to  the  sender  of  the  postal 
money  order,  page  242?  the  express  money  order,  page  243? 
the  telegraphic  money  order,  page  244?  the  bank  money  order, 
page  244? 

2.  What  will  be  the  total  cost  of  a  postal  money  order  for 
27^?  $2.19?  85.28?  810.40?  818.90?  845.10?  835.89?  8125 
(1100  +  825)?  875.29?  849.82?  8127.16? 

3.  What  will  be  the  total  cost  of  an  express  money  order  for 
86.20?  828.80?  819.50?  827.95?  848.90?  865  (850+815)? 
8111?  837.59?  841.72?  $65.59?  8114? 

4.  What  will  be  the  total  cost  of  a  telegraphic  money  order 
from  Boston  to  New  York  for  850?  875?  8100?  8125?  8150? 
8200?  8300?  8400?  8450?  8500?  from  Boston  to  Phila- 
delphia? from  Boston  to  San  Francisco?  from  Boston  to 
Chicago  ? 

5.  Translate  the  following  telegraphic  money  order :  Find- 
able  F.  J,  Reed^  20  Farh  St.  jicheron  findelkind.  How  much 
will  it  cost  for  such  an  order  from  Boston  to  Galveston?  from 
Boston  to  Chicago?  from  Rochester  to  Boston? 

WRITTEN  EXERCISE 

1.  Find  the  total  cost  of  5  postal  money  orders  for  the  fol- 
lowing amounts :  83.10;  88.19;  825.06;  818.50;  820. 

2.  Find  the  total  cost  of  six  express  money  orders  for  the 
following  amounts :  81.25;  810;  86.80;  816.25;  880;  819.50. 

3.  Find  the  total  cost  of  the  following  telegraphic  money 
orders:  one  from  Boston  to  New  York  for  850;  one  from 
Boston  to  Philadelphia  for  8500;  one  from  Boston  to  San 
Francisco  for  8175;  one  from  Boston  to  Galveston  for  8300; 
one  from  Boston  to  Rochester  for  8250. 


246 


CONCISE   BUSINESS   ARITHMETIC 


Checks  and  Baxk  Drafts 

272.  Business  men  usually  keep  their  money  on  deposit  with 
a  commercial  bank  or  trust  company  and  make  most  payments, 
at  home  and  at  a  distance,  by  check;  that  is,  an  order  on  a 
bank  from  one  of  its  depositors  for  the  payment  of  money. 


go^ton,  a^aisf^., 


^^7,     19 —   ^o./J'/ 


^ap  to  tjc  order  of^CT^Jj 


T^.^7^^^:^^^.<^^^  ^^\^ 


1=  aDoIIarjg 


A  check  may  be  drawn  for  any  amount  so  long  as  it  does  not  exceed 
the  balance  on  deposit  to  the  credit  of  the  drawer.  It  may  be  drawn 
payable  to :  (1)  the  order  of  a  designated  payee,  in  which  case  the  payee 
must  indorse  it  before  the  money  will  be  paid  over ;  (2)  the  payee,  or 
bearer,  in  which  case  any  one  can  collect  it;  (3)  "Cash,"  in  which  case 

any  one  can  collect  it. 

C.  B.  Sherman  &  Co.  and 
E.  H.  Robinson  &  Co.  in  the 
foregoing  check  both  reside 
in  Boston.  On  receiving  the 
check  E.  H.  Robinson  &  Co. 
indorse  it  and  deposit  it  for 
credit  with  their  bank,  say 
the  National  Shawmut  Bank. 
The  First  National  Bank  or 
the  National  Shawmut  Bank, 
as  well  as  each  of  the  other 
banks  in  the  city,  has  many 
depositors  who  draw  checks 
upon  it  which  are  deposited 
by  the  payees  in  various  other  city  banks ;  it  also  receives  daily  for  credit 
from  its  own  depositors  checks  drawn  upon  various  other  city  banks. 

Each  bank  therefore  has  a  daily  balance  to  settle  or  to  be  settled  with 
each  of  the  other  banks.  To  some  it  has  payments  to  make  and  from 
others  it  has  payments  to  receive.  If  these  balances  were  adjusted  in 
money,  each  bank  would  have  to  send  a  messenger  to  each  of  the  debtor 


Interior  View  or  a  Clearing  House 


EXCHAIS^GE  247 

banks  to  present  accounts  and  receive  balances.  This  would  be  a  risky 
and  laborious  task.  To  facilitate  the  daily  exchanges  of  items  and  settle- 
ments of  balances  resulting  from  such  exchanges  there  has  been  established 
in  every  large  city  a  central  agency,  called  a  clearing  house.  This  agency 
is  an  association  of  banks  which  pay  the  expense  of  conducting  it  in  pro- 
portion to  the  average  amount  of  their  clearings. 

Suppose,  for  example,  that  the  banks  constituting  a  clearing  house  are 
Nos.  1,  2,  3,  and  4.  No.  1  presents  at  the  clearing  house  items  against  Nos. 
2,  3,  and  4,  and  Nos.  2,  3,  and  4  present  items  against  No.  1.  So,  likewise, 
with  No.  2  and  each  of  the  other  banks.  In  the  clearing  house  there  are  usually 
two  longitudinal  columns  containing  as  many  desks  as  there  are  banks  in  the 
association.  At  a  given  time  a  settling  clerk  from  each  bank  takes  his  place 
at  his  desk  inside  of  one  of  the  columns  and  a  delivery  clerk  from  each  bank 
takes  his  place  outside  the  column.  Each  delivery  clerk  advances,  one  desk 
at  a  time,  and  hands  over  to  each  settling  clerk  his  exchange  items  against  that 
bank.  After  the  circuit  of  the  desks  has 
been  completed  each  delivery  clerk  is  at 
the  point  from  which  he  started,  and  each 
settling  clerk  has  on  his  desk  the  claims  of 
all  of  the  other  banks  against  his  bank. 
Each  settling  clerk  then  compares  his 
claims  against  other  banks  with  those  of 
other  banks  against  him  and  strikes  a 
balance.  This  balance  may  be  in  favor 
of  or  against  the  clearing  house.  If  No.  1  brought  claims  against  Nos.  2,  3, 
and  4  aggregating  ^211,000  and  Nos.  2,  3,  and  4  brought  claims  against 
No.  1  aggregating  $200,000,  there  is  $11,000  due  No.  1  from  the  clearing 
house.  But  if  No.  1  brought  to  the  clearing  house  exchange  items 
aggregating  $200,000  and  took  away  exchange  items  aggregating  $211,000, 
there  is  $11,000  due  the  clearing  house  from  No.  1.  So,  likewise,  with 
No.  2  and  each  of  the  other  banks.  When  all  of  the  exchanges  have 
been  completed,  the  clearing  house  will  have  paid  out  the  same  amount 
that  it  has  received. 

But  all  checks  received  by  banks  are  not  payable  in  the  city.  Suppose 
that  A.  W.  Palmer,  of  Chicago,  111.,  owes  C.  B.  Andrews,  of  Westfield, 
Mass.,  $500  and  that  the  amount  is  paid  by  a  check  on  the  City  National 
Bank  of  Chicago.  C.  B.  Andrews  receives  the  check  and  offers  it  for  credit  at 
the  Farmers  and  Traders  Bank  of  Westfield,  Mass.  The  Westfield  Bank  has 
no  account  with  any  Chicago  bank,  but  it  has  with  the  First  National  Bank 
of  Boston,  and  the  check  is  sent  to  that  bank  for  credit.  The  First  National 
Bank  wishes  to  increase  its  New  York  balance  and  the  check  is  forwarded 
to  Chemical  National  Bank  of  New  York  for  credit.  Chemical  National 
Bank  next  mails  the  check  to  Commercial  National  Bank  of  Chicago,  the 


248  CONCISE   BUSINESS    ARITHMETIC 

bank  with  which  it  has  regular  dealings  in  that  city.  Commercial 
National  Bank  sends  the  check  to  the  clearing  house  and  it  is  carried 
to  the  City  National  Bank  by  a  messenger  from  that  bank.  Thus,  all  of  a 
depositor's  checks  will  in  time  be  presented  to  the  bank  on  which  they  are 
drawn.  When  presented,  they  will  be  charged  to  the  depositor,  canceled, 
and  later  returned  to  him  to  be  filed  as  receipts. 

Banks  frequently  charge  their  depositors  a  small  fee  (rate  of  exchange) 
for  collecting  out-of-town  checks.  This  fee  is  rarely  over  ^i^%,  but  there  is 
no  uniformity  in  the  matter.  Sometimes  when  a  customer  keeps  a  large 
bank  account,  no  charge  whatever  is  made  for  the  collection. 

273.  It  often  happens  that  a  person  will  find  it  necessary  to 
make  payment  to  one  who  does  not  care  to  take  the  risk  of  a 
private  check  or  to  one  who  should  not  be  called  upon  to  pay 
the  cost  of  cashing  a  check.  In  such  cases  some  other  form  of 
instrument  of  transfer  must  be  used.  A  very  common  and  con- 
venient method  of  making  a  remittance  is  by  means  of  a  bank 
draft,  a  check  of  one  banking  institution  upon  another. 


Boston,  ^ass.^JUc^ / (^J9 J/o..^Z^ 

Uraders  >J\ationat  ^Jjank 

^aif  to  the  ort/er  of  ^~W.~^..  ~^ ^^^^^-g-^^^^T^ ^A^^^M 

Jo   CAemlcal  J/ationai  38ank\    ~;^^^'^^-r^y^^^ 

J/ew    York  j  ^  ^«*>'-'' 


Banks  in  the  different  cities  frequently  keep  running  accounts  with  each 
other  and  make  periodical  settlements.  At  the  time  of  drawing  the  above 
draft  Traders  National  Bank  of  Boston  very  likely  has  checks  and  drafts 
drawn  upon  New  York  banks  which  it  has  received  from  its  depositors. 
These  it  sends  to  Chemical  National  Bank  to  cover  the  amount  of  the  draft. 
Corresponding  transactions  may  also  take  place  in  New  York.  Chemical 
National  Bank  may  sell  its  draft  on  Traders  National  Bank  and,  to  cover 
the  amount,  remit  checks  and  drafts  on  Boston  banks  which  it  has  received 
from  its  depositors.  What  is  occurring  between  these  two  places  is  also 
occurring  between  many  other  places ;  but  drafts  upon  New  York  banks 
and  other  financial  centers  are  the  most  used  in  making  remittances. 


EXCHANGE  249 

A  bank  draft  is  sometimes  drawn  payable  to  the  one  to  whom  it  is  to  be 
sent.  It  is  better,  however,  to  have  it  drawn  payable  to  the  purchaser,  who 
may  indorse  it  over  to  the  person  to  whom  it  is  to  be  sent.  In  this  way 
the  name  of  the  sender  appears  on  the  draft,  and  when  canceled,  the  draft 
will  serve  the  purpose  of  a  receipt.  Banks  usually  sell  drafts  at  a  slight 
premium  on  the  face.  This  premium  is  called  exchange.  It  varies  some- 
what (see  page  254),  but  is  seldom  more  than  ■^-^%. 

274.  There  are  still  other  methods  of  transmitting  funds 
through  the  instrumentality  of  a  bank.  A  depositor  may  ex- 
change his  own  check  for  that  of  a  cashier's  check.  The  latter, 
being  a  check  of  the  cashier  on  his  own  bank,  would  pass  among 
strangers  better  than  a  depositor's  check. 


National  Shawtmut  Bank 


Boston,  Mass.,    J^^^^//,   19 No.di2^£/ 


]^«^the  order  oi~^..^.^<^^^S^^/\y/^^ 


In  New  York  City,  cashier's  checks  are  occasionally  used  instead  of  the 
New  York  draft.  As  New  York  exchange  is  in  demand  in  all  parts  of 
the  country,  the  expediency  of  the  course  is  apparent. 

275.  By  depositing  a  sum  of  money  in  a  bank  a  person  may 
receive  a  certificate,  called  a  certificate  of  deposit.  This  will 
direct  the  payment  of  the  sum  deposited  to  any  person  whom 
the  depositor  may  name. 


^:Jj2J2J2Jr-  SBoaton.  -M^.,,       (l^^^  /r     fO J^o.Z^f 

^^P^^  ^jyational  SLaivmut  38ank 

payahte  to  the  orcUf  nf  ^'~^./'^.'^^^^^^C^^^^^^<y7S^^ - 


on  the  return  of  this  certificate  properlif  indorsed. 


C^r^,.>^yr^^4::^--^^^^ 


The  payee  in  a  certificate  of  deposit  will  have  no  difficulty  in  getting  the 
certificate  cashed  or  the  amount  credited  to  him  by  his  bank. 


250  CONCISE   BUSINESS   ARITHMETIC 

ORAL    EXERCISE 

1.  Assuming  that  the  bank  which  cashed  the  check  on 
page  5  charged  i  %  collection,  what  was  the  amount  credited 
to  the  depositor? 

2.  Silas  Long  of  New  York  deposited  the  following  check. 
The  bank  deducted  yL.  %  for  collection.  How  much  was  placed 
to  Silas  Long's  credit  ? 


Cljt  ^niott  Bank 


150jgton,  0^agiEi., xvv^-g^^-^i 9 /i5o._^ 


l^ar  to  ti^e  otDet  of 


CjJ^^^^^r^Ah^^^^^^c/'T^-re^  /y^^. 


<^'f^yh. 


3.  B  deposited  three  out-of-town  checks  in  his  bank,  as  fol- 
lows: S300;  $700;  S750.  If  the  bank  charged  J^%  collec- 
tion, what  amount  was  placed  to  B's  credit  ? 

4.  Bring  to  the  class  a  number  of  canceled  checks,  and  take 
several  of  them  and  trace  them  from  the  time  they  were  issued 
until  they  were  filed  as  receipts  by  the  drawer.  Show  why  a 
canceled  check  is  the  best  kind  of  receipt  for  the  payment  of 
money  ? 

5.  How  much  did  the  bank  draft  on  page  248  cost  the  pur- 
chaser if  the  exchange  was  at  J^  %  premium  ? 

WRITTEN    EXERCISE 

1.  Find  the  cost  of  a  bank  draft  for  S  3958.75  at  yV  %  Pre- 
mium; of  a  bank  draft  for  $679.80  at  gV^  premium;  of  a 
bank  draft  for  $768.54  at  50/  per  $1000  premium. 

2.  To  cover  the  cost  of  a  bank  draft  bought  at  J^  %  premium, 
I  gave  my  bank  a  check  for  $250.25.  What  was  the  face  of 
the  draft  ?     What  was  the  rate  of  premium  per  $  1000  ? 


EXCHANGE 


251 


3.  How  large  a  bank  draft  can  be  bought  for  $850.85,  ex- 
change being  at  Jg-%  premium? 

4.  Find  the  proceeds  of  the  accompanying  deposit,  J^^  col- 
lection and  exchange  being  charged  on  the  out-of-town  checks. 

"When  the  receiving  teller  takes  a 
deposit  from  a  customer,  he  classi- 
fies the  items  on  the  deposit  ticket,  as 
shown  in  the  accompanying  illustra- 
tion. If  the  coin  and  bills  passed  in 
count  right,  these  items  are  checked 
(►^)  on  the  deposit  slip ;  if  a  check 
on  a  clearing  house  bank  is  received, 
it  is  marked  with  the  number  of  that 
bank  in  the  clearing  house ;  if  a 
check  on  the  teller's  bank  is  received, 
it  is  marked  "  B  " ;  if  a  check  on  an 
out-of-town  bank  is  received,  it  is 
marked  "X." 


THE   UNION    NATIONAL   BANK 

DEPOSITED   BY 


Boston, 


c^Cf^ 


cv^.  y,  /c 


Specie 

Bills  ....  ^^.^ 

Checks  .    .  -xdyLiz.<6i^4^^  .    >K/ 


2,^ 


2^ 


i^J /  7-7 


JS\ 


rdt^^ 


-///f^^J/ 


^(r^<1^AfrJk^\ 


fCjSJl. 


/  zr? 


^/L 


5.  AVrite  a  bank  draft,  using 
the  following  data:  your  ad- 
dress and  the  current  date;  drawer,  Central  National  Bank; 
drawee,  Chemical  National  Bank,  New  York  ;  amount,  $711.94  ; 
payee,  C.  E.  Denison ;  cashier,  your  name.  How  large  a  check 
will  pay  for  the  draft  at  J^- %  premium  ?     Write  the  check. 

6.  Suppose  that  the  members  of  the  class  whose  surnames 
begin  with  the  letters  from  A  to  G  inclusive  have  a  deposit  with 
Traders  National  Bank ;  that  the  members  whose  surnames 
begin  with  the  letters  from  H  to  N  inclusive  have  a  deposit 
with  City  National  Bank ;  that  the  members  whose  surnames 
begin  with  O  to  S  inclusive  have  a  deposit  with  First  National 
Bank ;  and  that  the  members  whose  surnames  begin  with  T  to  Z 
inclusive  have  a  deposit  with  Central  Bank.  Let  each  student 
write  ai  check  on  his  bank  in  favor  of  one  of  his  classmates, 
and  let  this  classmate  indorse  the  check  and  deposit  it  with  his 
bank.  Then  form  a  clearing  house,  strike  a  balance  between 
the  different  banks,  and  have  these  balances  adjusted  by  the 
payment  of  school  money. 


252  CONCISE   BUSINESS   ARITHMETIC 

Commercial  Drafts 

276.    Business  men  frequently  employ  the  commercial  draft 
as  an  aid  in  the  collection  of  accounts  that  are  past  due. 


/  2/^^.^^  --^c^^^.^^,^^.^^  ■  9, 1Q 


r^^-^T^^ 


•^A^^..<U 


U^^^^b^^,^!^^^  • ^qy  to  the  order  of 


Value  received  and  ckarye  to  account  of 

■Jo.    (^-^..f'^l^F^y^'^/^  .^/'J/  y^  /7  y^ 


-^ 


The  above  is  a  common  form  of  draft  used  for  collection  purposes. 
Edgar  McMickle  owes  Wilbert,  Gloss  &  Co.  %  260.50.  The  amount  is  due, 
and  Wilbert,  Closs  &  Co.  draw  a  draft  on  Edgar  McMickle  and  leave  it  with 
their  Springfield  bank  for  collection.  The  Springfield  bank  forwards  it  to 
its  correspondent  in  Paterson,  and  this  bank  sends  it  by  messenger  to  Edgar 
McMickle.  When  he  pays  the  draft  the  Paterson  bank  notifies  the  Spring- 
field bank,  and  that  bank  deducts  a  small  fee  (collection  and  exchange)  for 
collecting  the  draft,  and  credits  Wilbert,  Closs  &  Co.  for  the  proceeds. 

277.  It  has  been  seen  (page  231)  that  the  time  draft  is  fre- 
quently used  in  connection  with  sales  of  merchandise. 


:'^::^'^^-^^^  .g?^-^,.^^  ^,^^^..-^.^}^:Zf:?^7t'^  ^^y  to  the  order  of 


Value  received  and  charge  to  account  of 

Jo^ ^-^."M^^^^ ;^7^ ^    ,       ^        .  ^^ 


Suppose  Quincy,  Bradley  &  Co.  sell  L.  B.  Wade  &  Co.  a  bill  of  merchan- 
dise amounting  to  $500.  Terms :  30-da.  draft  for  the  amount  of  the  bill. 
The  draft,  as  above,  and  the  bill  in  regular  form  would  be  di*awn  up  and 


EXCHANGE  253 

sent  to  L.  B.  Wade  &  Co.  for  acceptance.  The  object  of  drawing  a  time 
draft  in  connection  with  sales  of  merchandise  is  twofold:  (1)  when  ac- 
cepted, the  draft  serves  as  a  written  contract;  (2)  since  an  acceptance  is 
negotiable,  it  may  be  discounted  and  cash  realized  upon  it  before  maturity. 
Such  a  draft  is  frequently  left  with  a  bank  for  collection  instead  of  being 
remitted  with  the  bill.  The  bank  will  then  first  present  the  draft  for  accept- 
ance and  later  for  payment. 

ORAL  EXERCISE 

1.  If  you  exchange  your  check  for  a  cashier's  check,  is  there 
any  charge  for  the  accommodation  ? 

2.  If  the  sight  draft  on  page  252  was  collected  by  a  bank 
which  charged  J%  collection,  how  much  was  placed  to  the 
credit  of  Wilbert,  Closs  &  Co.? 

3.  You  deposited  in  Shawmut  National  Bank  $5000,  received 
the  certificate  of  deposit  shown  on  page  249,  and  remitted  it 
to  E.  B.  Stanton  on  account.      Would  there  be  any  exchange  ? 

WRITTEN  EXERCISE 

1.  The  draft  on  page  252  was  accepted  July  17,  and  dis- 
counted July  25.  If  the  bank  charged  J^  %  collection  and 
6  %  interest,  how  much  was  placed  to  the  credit  of  the  drawers  ? 

2.  Mar.  27  Wilson  Bros.,  Chicago,  111.,  drew  a  30-da.  draft 
on  E.  W.  King,  Toledo,  O.,  in  favor  of  themselves,  payable  30  da. 
after  date,  for  §3500,  and  mailed  it  for  acceptance.  Apr.  1  the 
draft  was  received  accepted;  Apr.  2  it  was  discounted  at  City 
Bank.  If  the  charges  were  gV  %  collection  and  6  %  interest, 
what  amount  was  credited  to  AVilson  Bros.? 

3.  Apr.  17  O.  H.  Brooks,  Buffalo,  N.Y.,  drew  a  sight  draft 
on  Slocum  &  Co.,  Hartford,  Conn.,  in  favor  of  himself,  for  $391, 
and  left  it  with  his  bank  (First  National)  for  collection.  First 
National  Bank  sent  the  draft  to  its  Hartford  correspondent 
(Commercial  National),  and  5  da.  later  informed  O.  H.  Brooks 
that  the  draft  had  been  collected,  and  the  amount,  less  \  %  col- 
lection, placed  to  his  credit.  If  O.  H.  Brooks's  bank  balance 
was  $758.62  before  the  draft  was  drawn,  what  was  it  after  the 
draft  was  credited  ?    Write  the  draft  and  show  the  indorsements. 


254  CONCISE   BUSINESS   ARITHMETIC 

4.  Aug.  9  you  sold  C.  D.  Mead  &  Co.,  San  Francisco,  Cal., 
39  mahogany  sideboards  at  i  162. 50,  delivered  the  goods  to  the 
Interstate  Transportation  Co.,  and  received  a  through  bill  of 
lading  (receipt  for  the  goods  and  an  agreement  to  transport 
and  deliver  them  to  the  consignee  or  to  his  order).  You  then 
drew  a  sight  draft  on  C.  D.  Mead  &  Co.  in  favor  of  your  bank, 
attached  the  draft  to  the  bill  of  lading,  and  left  it  with  your 
bank  for  collection.  Your  bank  indorsed  the  draft  and  the  bill 
of  lading  and  sent  them  to  First  National  Bank  of  San  Fran- 
cisco for  collection  and  credit.  Aug.  23  you  received  advice 
that  the  draft  had  been  collected,  and  the  amount,  less  |  %, 
placed  to  your  credit.    What  was  the  amount  credited  ? 

When  First  National  Bank  of  San  Francisco  received  the  draft,  it  notified 
C.  D.  Mead  &  Co.  They  paid  the  draft,  and  the  bank  gave  them  the  bill  of 
lading.  When  goods  are  shipped  in  this  manner,  the  transportation  company 
will  not  deliver  the  goods  until  the  consignee  presents  the  bill  of  lading. 

Fluctuation  of  Rates  of  Exchange 

278.  It  has  been  seen  that  money  orders  always  sell  for  more 
than  their  face  value,  and  that  bank  drafts  frequently  cost  a 
little  more  than  their  face  value.  When  exchange  costs  its 
face  value,  it  is  said  to  be  at  par ;  when  it  costs  more  than  its 
face  value,  it  is  said  to  be  at  a  premium ;  when  it  costs  less  than 
its  face  value,  it  is  said  to  be  at  a  discount. 

On  bank  drafts  for  small  sums,  say  $  500  or  less,  exchange  is  usually  at 
a  uniform  premium.  This  premium  is  to  pay  the  banks  for  their  trouble 
and  the  expense  of  shipping  money  to  the  centers  on  which  the  drafts  are 
drawn,  when  balances  at  these  points  become  low.  But  exchange  on  the 
trade  centers  of  the  country  may  be  at  par  at  one  time,  at  a  premium  at 
another,  and  at  a  discount  at  still  another.  For  example,  during  the  late 
fall  months,  when  the  grain  crops  begin  to  be  sent  East,  New  York  is  send- 
ing a  great  many  checks  and  drafts  to  the  section  of  which  Chicago  is  the 
trade  center.  Exchange  on  New  York  is  then  very  plentiful  in  Chicago,  and 
if  a  man  in  Chicago  wished  to  buy  a  draft  on  New  York  for  a  large  amount, 
say  $  10,000  or  more,  the  Chicago  banks  will  sell  it  to  him  at  a  discount. 
But  if  a  man  in  New  York  at  that  time  wished  to  buy  a  draft  on  Chicago 
for  $10,000,  he  would  have  to  pay  a  premium,  because  the  New  York 
banks  would  be  anxious  not  to  decrease  their  Chicago  balances. 


EXCHANGE  255 

Early  in  the  spring,  when  New  York  importers  and  jobbers  are  sending 
foreign  and  domestic  manufactured  goods  for  distribution  in  the  West,  a 
great  many  checks  and  drafts  are  being  sent  from  the  West  to  New  York,  and 
exchange  is  at  a  discount  in  New  York  and  at  a  premium  in  Chicago.  This 
principle  applies  at  all  trade  centers  between  which  exchange  operations  go 
on.  Smaller  places  make  their  settlements  in  or  through  larger  places,  and 
the  main  exchange  transactions  go  on  between  the  few  leading  cities,  with 
converging  lines  on  New  York. 

The  rate  of  exchange  between  two  cities  will  never  exceed  the  cost  of 
shipping  actual  money  from  one  of  the  cities  to  the  other,  except  in  time  of 
panic  or  a  financial  unrest.  Thus  when  the  cost  of  sending  money  by  express 
from  New  York  to  Chicago  is  $5  per  ^  10,000,  the  discount  in  New  York  or 
the  premium  in  Chicago  will  not  greatly  exceed  ji^  %  (|  5  per  $  10,000) . 
To  prevent  the  rates  from  going  any  higher  the  banks  will  arrange  for  the 
shipment  of  actual  money  from  New  York  to  Chicago. 

As  a  rule  no  charge  is  made  for  cashing  bank  drafts  on  the  trade  centers 
of  the  country,  like  New  York,  Chicago,  and  Philadelphia. 

279.  It  has  been  seen  that  banks  frequently  charge  a  small 
fee  for  collecting  paper  payable  out  of  town. 

In  some  cases  the  rates  of  collection  are  more  or  less  arbitrary ;  in  others 
they  are  governed  by  trade  movements,  the  same  as  rates  of  exchange.  In 
still  others  the  clearing  house  association  fixes  the  rate. 

ORAL  EXERCISE 

Find  the  cost  of  the  following  hank  drafts: 

1.  8 18,500  at  2V  %  discount ;  at  40  ^  per  $  1000  premium. 

2.  $  516.90  at  Jq  %  premium  ;  at  50  ^  per  $  1000  discount. 

3.  81600.80  at  75^  per  81000  premium  ;  at  -^^  %  discount. 

4.  A  draft  for  $4000  was  bought  for  8  3998.  Was  ex- 
change at  a  premium  or  at  a  discount,  and  what  rate? 

5.  J.  E.  Smith  &  Co.  drew  at  sight  on  E.  M.  Barrows  for 
8250  and  made  collection  through  their  bank.  If  the  bank 
charged  ^L  ^  for  collection,  for  what  amount  did  J.  E.  Smith 
&  Co.  receive  credit  ? 

6.  During  the  late  fall  many  checks  and  drafts  are  being 
sent  to  the  southern  cities  in  payment  for  shipments  of  cotton. 
At  such  times  is  exchange  on  New  York  likely  to  be  at  a  dis- 
count or  at  a  premium  in  New  Orleans  ?  in  New  York  ? 


DIVIDENDS   AND   INVESTMENTS 
CHAPTER  XXI 

STOCKS  AND   BONDS 
STOCKS 

280.  A  corporation,  or  stock  company,  is  an  association  of  indi- 
viduals organized  under  the  laws  of  a  particular  state  into  a 
body  which  is  by  law  given  the  rights  and  powers  and  civil 
liabihties  of  a  person. 

Being  a  mere  creature  of  law  a  corporation  possesses  only  those  proper- 
ties which  its  charter  (the  instrument  which  defines  its  rights  and  duties) 
confers  upon  it.  These  are  such  as  are  best  calculated  to  effect  the  object 
for  which  it  was  created.  Among  the  most  important  is  legal  continuous 
existence,  irrespective  of  that  of  the  individuals  composing  it. 

281.  The  capital  stock  of  a  corporation  represents  the  interest 
of  the  individuals  who  compose  the  corporate  body  in  the  prop- 
erty and  profits  of  the  corporation. 

The  capital  stock  is  divided  into  a  definite  number  of  shares.  It  is  not 
necessary  to  give  these  shares  a  par  value,  but  it  is  customary  to  do  so. 
The  usual  par  value  of  a  share  is  SIOO.  However,  any  amount  may  be  the 
par  value. 

282.  A  stock  certificate  is  a  legal  instrument  which  evidences 
that  the  holder  owns  a  certain  number  of  shares  of  stock  in  the 
corporation  or  association  issuing  the  certificates.  A  stockholder 
is  a  person  who  owns  one  or  more  shares  of  stock. 

The  certificate  bears  the  seal  of  the  corporation  and  is  signed  by  officers 
(usually  the  president  and  the  treasurer  or  their  representatives)  authorized 
by  the  by-laws  to  sign  stock  certificates. 

Stockholders  elect  a  few  of  their  number  to  have  general  control  of  the 
company.  The  stockholders  thus  elected  constitute  the  board  of  directors. 
This  board  may  delegate  its  powers  to  several  of  its  members  called  an 
executive  committee.  The  control  of  a  corporation  is  vested  in  its  board 
of  directors. 

266 


STOCKS   AND   BONDS 


257 


283.  A  dividend  is  a  sum  of  money  paid  by  a  corporation  to 
its  stockholders,  each  share  participating  equally.  An  assess- 
ment is  an  amount  per  share  which  stockholders  are  called  upon 
to  pay  to  make  up  losses  or  deficiencies. 

The  board  of  directors  decide  upon  the  rate  of  dividend,  which  usually 
means  the  rate  per  annum  on  the  face  value  of  the  stock,  but  it  may  also  be 
expressed  as  a  certain  amount  in  dollars  and  cents  per  share. 

Shares  of  stock  may  be  non-assessable. 

284.  A  company  may  divide  its  stock  into  two  or  more  classes; 
the  usual  division  is  preferred  and  common. 


285.  Preferred  stock  is  stock  which  is  entitled,  out  of  profits, 
to  a  preferential  dividend  at  a  fixed  rate.  In  case  a  company 
is  dissolved,  its  preferred  stock  usually  has  a  preferential  claim 
against  the  assets  of  the  company  up  to  the  par  value  of  the 
preferred  stock  outstanding. 

The  prior  rights  of  preferred  stocks  over  common  usually  make  them 
safer  investments,  but  stocks  are  not  necessarily  safe  because  preferred. 


258 


CONCISE   BUSINESS  ARITHMETIC 


286.  Common  stock  is  the  stock  wliich  has  the  right  to  the 
equity  in  the  earnings  and  the  income  of  the  hquidation  in  the 
assets  of  a  corporation  after  the  claims  of  all  prior  security 
issues  (bonds,  notes,  preferred  stock,  etc.)  have  been  satisfied. 


287.  The  par  value  is  the  face  value  of  stocks;  the  market 
value  is  the  sum  for  which  the  stocks  can  be  sold  in  the  market. 

288.  If  a  company  is  prosperous  and  pays  a  higher  rate  of 
dividend  than  the  money  could  earn  with  no  greater  risk  in  the 
general  money  market,  a  share  may  sell  for  more  than  its  face 
value ;  it  is  then  said  to  be  above  par^  or  at  a  premium.  If  the  com- 
pany pays  a  lower  rate  of  dividend  than  could  be  obtained  at  no 
greater  risk  in  the  general  money  market,  a  share  may  sell  for 
less  than  its  face  value ;  it  is  then  helow  par^  or  at  a  discount 

289.  A  stock  broker  is  a  person  who  buys  and  sells  stocks  for 
other  persons  on  commission. 

Stocks  are  usually  bought  and  sold  through  stock  brokers.  The  broker's 
commission  is  usually  ^%  of  the  par  value  of  the  stock,  or  12^^  per  share. 
A  charge  is  made  for  either  buying  or  selling. 


STOCKS   AND   BONDS  259 

290.  When  the  price  of  stock  is  quoted  at  97,  118|,  1601 
it  means  that  a  share  whose  par  value  is  $100  can  be  bought 
for  $97,  $118.75,  $160.50.  If  a  person  buys  stock  through  a 
broker  at  1601,  it  will  cost  him  $160.50  +  $0,121  brokerage,  or 
$160,621;  if  he  sells  stock  through  a  broker  for  1601,  he  will 
receive  as  proceeds  $160.50  -  $0,121,  or  $160,371,  per  share. 

On  the  New  York  Stock  Exchange  quotations  are  expressed  in  dollars 
and  eighths  of  a  dollar. 

In  some  other  cities  quotations  are  expressed  in  dollars,  in  eighths  of  a 
dollar,  and  in  sixteenths  of  a  dollar.  When  stocks  are  quoted  at  less  than 
$1  per  share,  fluctuations  are  sometimes  expressed  in  cents. 

The  bulk  of  transactions  in  the  stock  exchanges  is  in  round  lots.  In 
New  York  round  lots  are  100  shares  or  some  multiple  thereof ;  in  Boston, 
50  shares  or  some  multiple  thereof.  In  these  cities  any  other  number  of 
shares  than  the  ones  named  for  each  would  be  called  odd  lots.  In  Chicago 
no  distinction  is  made  between  round  and  odd  lots.  Fractional  shares  of 
stock  which  are  occasionally  in  the  market  are  called  scrip. 

ORAL   EXERCISE 

1.  Examine  the  certificate  of  stock,  page  257.  What  is  the 
name  of  the  company  ?  From  whom  did  the  company  get  its 
right  to  carry  on  business  as  a  corporation  ? 

2.  What  is  the  entire  capital  stock  of  the  company  ?  Into 
how  many  shares  is  this  divided  ?  What  per  cent  of  the  entire 
stock  of  the  company  does  the  holder  of  the  certificate  own  ? 

3.  What  kind  of  stock  is  represented  by  the  certificate? 
What  is  the  difference  between  common  and  preferred  stock? 

4.  What  is  the  par  value  of  each  share  ?  If  the  market  value 
of  each  share  is  $160,  what  is  the  certificate  worth  ? 

5.  What  sum  must  be  laid  aside  to  provide  for  the  dividends 
on  the  preferred  stock  of  the  company,  the  rate  being  6  %  ?  How 
much  of  this  sum  will  the  holder  of  the  certificate  receive  ? 

6.  Examme  the  stock  certificate,  page  258.  What  part  of 
the  stock  of  the  company  is  common  stock  ? 

7.  A  5  %  dividend  on  the  common  stock  would  require  how 
much  money  from  the  treasury  of  the  company  ?  Of  this  sum 
how  much  would  George  W.  Putnam  receive  ? 


260 


CONCISE   BUSINESS   ARITHMETIC 


Dividends  and  Assessments 
written  exercise 

Unless  otherwise  specified,  the  par  value  of  a  share  will  be  understood 
to  be  .1100. 

1.  A  company  with  $3,500,000  capital  declares  an  8%  divi- 
dend.    What  does  the  holder  of  250  shares  receive  ? 

2.  B  holds  450  shares  of  Lehigh  Valley  Railroad  stock.  When 
the  company  declares  a  dividend  of  7J%,  how  much  will  he 
receive  ? 

3.  What  annual  income  is  derived  from  investing  $48,000 
in  Union  Pacific  Railroad  stock  at  120  if  2|%  semiannual 
dividends  are  declared  ? 

4.  E.  H.  Rhodes  holds  600  shares  of  Lehigh  Valley  Rail- 
road stock.  If  he  received  the  following  check  as  his  annual 
dividend,  what  was  the  rate  ? 


^.^^S^ay  to  /■/JjLfe- 


K/Ae  3'irst  >^ational  SBank 

i 


J/o.A2=lZ 


-/^/g?^  — 


a>ioi€Und  J{o.A^ 


reasurer 


5.  A  company  with  $1,000,000  capital  declares  quarterly 
dividends  of  1^%.  What  are  the  annual  dividends  ?  What  is 
the  amount  received  annually  by  D,  who  owns  475  shares  ? 

6.  A  corporation  with  a  capital  of  $125,000  loses  $2500. 
What  per  cent  of  his  stock  must  each  stockholder  be  assessed 
to  meet  this  loss  ?  How  much  will  it  cost  A,  who  owns  150 
shares  ? 

7.  A  company  with  a  capital  of  $750,000  declares  a  semi- 
annual dividend  of  3|%.  How  much  money  does  it  distribute 
annually  among  its  stockholders  ?  What  is  the  annual  income 
of  a  man  who  owns  200  shares  ? 


STOCKS   AND  BONDS  261 

8.  If  the  Pennsylvania  Railroad  declares  a  semiannual  divi- 
dend of  21%  on  a  capital  stock  of  $500,000,000,  what  amount 
is  annually  distributed  among  the  stockholders  ?  What  is  the 
annual  income  to  J.  P.  Morgan  from  this  stock  if  he  owns 
7,500,000  shares  having  a  par  value  of  |50  each? 

9.  During  a  certain  year  a  manufacturing  concern  with 
a  capital  of  $750,000  earns  $75,500  above  all  expenses.  It 
decides  to  save  $15,500  of  this  for  emergencies  and  to  divide 
the  remainder  in  dividends.  What  is  the  rate  ?  What  would 
be  the  amount  of  A's  dividend  check  if  he  owns  125  shares  ? 

10.  The  capital  stock  of  the  Gramercy  Finance  Company  is 
$1,500,000.  The  gross  earnings  of  the  company  for  a  year  are 
$375,000  and  the  expenses  $215,000.  What  even  per  cent  of 
dividend  may  be  declared  and  what  would  be  the  amount  of  un- 
divided profits  if  10%  of  the  net  earnings  are  first  set  aside  as  a 
surplus  fund  ?   (An  even  per  cent  is  a  per  cent  without  a  fraction.) 

11.  A  railway  company  has  a  capital  of  $3,500,000  and 
declares  dividends  semiannually.  During  the  period  from 
Jan.  1  to  July  1  of  a  certain  year  the  net  earnings  of  the  com- 
pany were  $191,000.  Of  this  amount  10  %  is  carried  to  surplus 
fund.  What  even  rate  per  cent  of  dividend  may  be  declared  on 
the  balance  and  how  much  will  be  carried  to  undivided  profits  ? 

12.  A  company  with  a  capital  stock  of  $500,000  gains  during 
a  certain  year  $38,750.  It  decides  to  carry  $5000  of  the 
profits  to  surplus  fund  and  to  declare  an  even  per  cent  of 
dividends  on  the  remainder.  What  sum  was  divided  among 
the  stockholders,  and  what  sum  was  carried  to  undivided 
profits  account  ?  What  was  the  annual  income  to  F  from  this 
stock  if  he  owned  500  shares  ? 

13.  During  a  certain  year  the  gross  earnings  of  a  railroad 
having  a  capital  stock  of  $100,000,000  were  $65,150,000,  and 
the  operating  expenses  $45,150,000.  If  the  company  declared 
a  semiannual  dividend  of  3J  %  and  carried  the  balance  of  the 
net  earnings  to  undivided  profits  account,  how  much  was 
divided  among  the  stockholders  ?  How  much  was  the  working 
capital  of  the  company  increased  ? 


262 


CONCISE   BUSINESS   ARITHMETIC 


14.  The  capital  stock  of  the  First  National  Bank  is  $  3,000,000, 
and  dividends  are  declared  semiannually.  The  profits  of  the 
bank  for  a  certain  six  months  are  $185,750.  Of  this  sum  10%  is 
carried  to  a  surplus  fund.  The  directors  then  vote  to  declare  a 
semiannual  dividend  of  3^%  and  carry  the  balance  of  the  profits 
to  undivided  profits  account.  What  amount  was  carried  to  surplus 
fund  account?  to  dividend  account?  to  undivided  profits  account? 

Buying  and  Selling  Stock 

291.  The  following  is  an  abbreviated  form  of  the  stock  quo- 
tations for  a  certain  day  on  the  New  York  Stock  Exchange : 


Table  op  Sales  and 

Range 

OF  Prices 

Sales 

Stocks 

Open. 

High. 

Low. 

Clos. 

Net  Change 

2,600 

Am.  Sugar.     .     .     . 

lOOi 

100^ 

99i- 

99f 

-f 

200 

Am.  Sugar  (pfd.)      . 

110 

llOi 

109i 

109i 

-i 

10,200 

Atchison     .... 

95^ 

95i 

91f 

92 

-H 

300 

Atchison  (pfd.)     .     . 

100 

100 

100 

100 

900 

At.  Coast  Line     .     . 

121i 

120 

116 

116 

-^ 

13,600 

Baltimore  &  0.     .     . 

m 

88f 

87i 

88 

-i 

600 

Baltimore  &0.  (pfd.) 

80i 

81 

80i 

80i 

-i 

147,100 

Canadian  Pacific .     . 

1931- 

200f 

1881 

1891 

-Si 

20,200 

Chic.  M.  &  St.  P.       . 

98| 

98i 

94i 

95 

-3f 

300 

Chic.  M.&  St.  P.  (pfd.) 

13  7f 

135 

134| 

1341 

-2 

200 

General  Chem.  (pfd.) 

108 

109 

108i 

109 

+  1 

2,500 

General  Electric  .     . 

144 

144 

141 

141 

-3 

15,600 

Gt.  Northern  (pfd.)  . 

122 

1211- 

119 

im 

-H 

1,600 

Illinois  Central     .     . 

110 

110 

107i 

107| 

-2f 

59,800 

Lehigh  Valley      .     . 

136i 

136^ 

132ir 

134f 

-If 

650 

Louisville  &  Nash.     . 

135f 

135i 

131i 

131ir 

-4i 

2,100 

Nat'l  Biscuit   .     .     . 

131 

130i 

125 

125 

-5 

100 

Nat'l  Biscuit  (pfd.)  . 

123 

1231 

1231- 

1231 

+  1 

69,200 

South.  Pacific .     .     . 

92|r 

91i 

86i 

87i 

-^ 

300 

South.  Pacific  (pfd.) . 

lOOi" 

97i 

97i 

97i 

-21 

210,100 

Union  Pacific  .     .     . 

154i 

154J 

1481 

1491 

-4 

400 

Union  Pacific  (pfd.) . 

82i 

82^ 

82 

82 

-i 

390,100 

U.S.  Steel  .... 

58i 

58f 

56 

56f 

-2f 

4,200 

U.S.  Steel  (pfd.)  .     . 

109 

109i 

107i 

107i 

-li 

In  the  first  column  is  shown  the  number  of  shares  of  stock  sold ;  in  the 
second,  the  name  of  the  stock ;  in  the  third,  fourth,  fifth,  and  sixth,  respec- 
tively, the  opening,  the  highest,  the  lowest,  and  the  closing  prices  of  the  day; 
in  the  last,  the  net  changes  betw:een  the  closing  price  of  yesterday  and  to-day. 
Thus,  2600  shares  of  American  Sugar  stock  were  sold.  The  opening  price 
was  $100.50  per  share;  the  highest  price  $100.50;  the  lowest,  $99.25  ;  the 
closing,  $99.75,  w^hich  shows  a  decline  of  75^  from  the  preceding  day. 


STOCKS  AKD  BOKDS  263 

ORAL   EXERCISE 

1.  Find  in  the  table  (page  262)  three  cases  where  a  quo- 
tation both  for  common  stock  and  for  preferred  (^pfd,  stands 
for  preferred)  stock  of  the  same  company  is  given.  Which  is 
worth  the  more  in  each  case  ?  The  par  value  of  all  shares  is 
$100. 

If  the  profits  of  a  concern  are  so  great  that  a  large  per  cent  may  be  paid 
on  the  common  stock,  after  paying  the  fixed  rate  on  the  preferred  stock, 
then  the  common  stock  may  sell  for  a  higher  figure  than  the  preferred. 

2.  What  would  100  shares  of  American  Sugar  (common)  cost 
if  bought  through  a  broker  at  the  lowest  price  for  the  day, 
brokerage  being  |^%. 

3.  What  would  the  seller  of  the  stock  realize  on  the  sale  ? 

Suggestion.  The  seller  would  receive  the  price  for  which  it  was  sold 
minus  the  brokerage,  i%. 

4.  State  the  cost,  at  the  opening  price  in  the  table,  of  100 
shares  each  of  the  following  stocks,  assuming  that  the  transac- 
tions take  place  through  a  broker  who  charges  ^  %  commission : 
Baltimore  &  Ohio ;  Canadian  Pacific ;  General  Electric ;  Lehigh 
Valley.     (Base  the  calculations  on  the  common  stock.) 

5.  At  the  highest  price  in  the  table,  state  the  amount  that 
would  be  received  from  the  sale  of  100  shares  of  each  of  the 
following  stocks,  assuming  that  they  were  sold  through  a  broker 
who  charged  1%  commission:  Southern  Pacific;  U.S.  Steel  (pre- 
ferred) ;  Great  Northern  (preferred) ;  National  Biscuit ;  Ameri- 
can Sugar  (preferred) ;  Atchison  ;  General  Chemical  (preferred) ; 
Illinois  Central;  Union  Pacific.  (If  preferred  is  not  named, 
common  stock  is  referred  to.) 

WRITTEN   EXERCISE 

Find  the  coat,  at  the  closing  price  in  the  table,  of  2500  shares  of 
the  following  stocks,  inclvding  brokerage  : 

1.  Canadian  Pacific.  4.   Baltimore  &  Ohio  (pfd.). 

2.  American  Sugar  (pfd.).        5.    Atlantic  Coast  Line. 

3.  National  Biscuit  (pfd.).       6.    United  States  Steel  (pfd.). 


264  CONCISE   BUSINESS   AEITHMETIC 

At  the  closing  price  for  the  day  find  the  amount  received  from 
the  sale  of  3500  shares  of  the  following  stocks  sold  through  a  broker: 

7.  Illinois  Central.  11.  Atchison  (pfd.). 

8.  Louisville  &  Nashville.  12.  General  Electric. 

9.  Southern  Pacific.  13.  Southern  Pacific  (pfd.). 
10.  Lehigh  Valley.  14.  Great  Northern  (pfd.). 

292.  Example.  I  bought  1000  shares  Chicago,  Milwaukee,  & 
St.  Paul  preferred  stock,  at  the  lowest  price  in  the  table,  and 
sold  the  same  at  140  i-.    Allowing  for  brokerage  both  for  buying 

and  selling,  did  I  gain  or  lose,  and  how  much  ? 

S140  37I- 
SoLUTiON.     Since  I  bought  through  a  broker,  each  share  *      2 

cost  me  ^  134.871  +.  $0.12^,  or  $  135  ;  and  since  I  sold  through  12>b.00 

a  broker,  the  proceeds  of  each  share  sold  was  $140.50  —  $0.12i,  $  5.371 

or  $140.37|.     $140,371  -  $135.00  =  $5.37|,   gain  on  each  1000 

share.     Since  $5.37^  is  gained  on  each  share,  1000  times    ■    ^      ^ 

$5.37^,  or  $5375,  is  gained  on  1000  shares.  ^o61b. 

In  the  following  exercise  it  is  understood  that  all  sales  and  jDurchases  are 
made  through  a  broker,  who  charges  a  commission  of  ^%  both  for  buying 
and  for  selling. 

WRITTEN    EXERCISE 

Find  the  gain  or  loss  on  500  shares  of  each  of  the  following  stocks 
bought  at  the  opening  price  and  sold  at  the  price  here  given : 

1.  Illinois  Central,  108|.  5.  American  Sugar  (pfd.),  103. 

2.  General  Electric,  147|.  6.  National  Biscuit,  1341. 

3.  Southern  Pacific  (pfd.),  89.        7.  Baltimore  &  Ohio,  90f . 

4.  General  Chemical  (pfd.),  110.    8.  Canadian  Pacific,  2001. 

9.  United  States  Steel  (pfd.),  112^. 

10.  Atlantic  Coast  Line,  115|. 

11.  Great  Northern  (pfd.),  125. 

12.  National  Biscuit  (pfd.),  126J. 

13-24.  Find  the  gain  or  the  loss  on  1000  shares  of  each  of 
the  above  stocks  bought  at  the  lowest  price  and  sold  at  the 
highest  price,  in  the  table. 

25.  John  R.  West  bought  400  shares  of  United  States  Steel, 
(common)  at  the  opening  price  in  the  table  and  sold  it  so  as  to 
gain  S300.     What  was  the  quoted  price  when  he  sold  it? 


STOCKS   AND   BONDS  265 

26.  I  bought  some  United  States  Steel  (preferred)  at  the 
opening  price  in  the  table  and  sold  it  for  112i.  If  I  gained 
$650  by  the  transaction,  how  many  shares  did  I  buy? 

27.  I  bought  2500  shares  of  General  Electric  at  the  lowest 
price  in  the  table,  held  it  for  a  year,  received  5  %  in  dividends, 
and  then  sold  it  at  139|^.  If  money  was  worth  41  %,  did  I  gain 
or  lose,  and  how  much  ? 

The  interest  is  to  be  computed  on  the  cost  of  the  stock,  the  dividend  on 
the  par  value. 

28.  I  gave  my  broker  orders  to  buy  1500  shares  of  Atchison 
(preferred)  and  to  sell  2000  shares  of  Canadian  Pacific.  If  he 
bought  at  the  lowest  price  in  the  table  and  sold  at  the  highest 
price,  what  balance  will  he  put  to  my  credit  ? 

BONDS 

293.  A  bond  is  an  instrument  by  which  a  government,  a 
municipality,  or  a  corporation  contracts  and  agrees  to  pay  a 
specified  sum  of  money  on  a  given  date,  at  a  specified  rate  of 
interest.  —  Rollins. 

Bonds  are  generally  issued  at  a  face  vailue  of  $  1000 ;  less  frequently,  of 
$500  ;  occasionally,  of  $100.  All  bonds  of  the  same  issue  usually  have  the 
same  rights  and  security. 

Bonds,  the  payment  of  which  depends  only  on  the  unsecured  credit  of 
the  issuing  company,  are  called  debenture  bonds;  those  that  have  their  pay- 
ment secured  by  a  mortgage  on  the  property  of  the  issuing  corporation 
are  called  mortgage  bonds;  those  that  are  secured  by  a  deposit  with  a  trustee 
of  collateral  are  called  collateral  trust  bonds ;  those  that  provide  that  the 
interest  on  them  shall  be  paid  only  if  earned  are  called  income  bonds. 

Bonds  of  a  national  government  are  called  government  bonds;  of  a  state, 
a  city,  a  town,  or  other  municipal  organization,  municipal  bonds. 

The  names  of  the  different  government  bonds  are  usually  derived  from 
the  interest  they  bear  and  the  time  when  they  mature.  Thus,  "  U.  S.  2s, 
1930,"  are  United  States  bonds  bearing  interest  at  2  %  and  maturing  in  1930. 

From  the  gross  earnings  of  a  company  the  operating  expenses  are  first 
deducted;  from  the  net  earnings  are  deducted  all  fixed  charges,  such  as 
interest  on  bonds;  then  the  dividends  on  preferred  stock  are  paid;  and 
finally  out  of  the  remainder  dividends  on  the  common  stock  are  paid. 


266 


CONCISE   BUSINESS  ARITHMETIC 


294.  With  reference  to  the  form  of  contract  for  the  payment 
of  principal  and  interest  there  are  two  kinds  of  bonds:  coupon 
and  registered. 


295.  A  coupon  bond  is  a  bond  to  which  are  attached  interest 
notes,  or  coupons,  representing  the  interest  due  on  the  bond  at 
stated  periods  of  payment. 


STOCKS   AND   BONDS  267 

The  interest  notes  may  be  cut  off  from  the  bonds  at  maturity  and  the 
amount  of  interest  which  they  represent  collected  through  a  bank.  If  these 
notes  are  not  paid  when  due,  they  bear  interest  at  the  legal  rate. 

296.  A  registered  bond  is  a  bond  which  has  no  separate  con- 
tract for  the  payment  of  the  interest.  Such  a  bond  must  be 
recorded  on  the  books  of  the  corporation  in  the  name  of  the 
holder  to  whom  the  interest  is  sent  by  check. 

Coupon  bonds  may  be  made  payable  either  to  bearer  or  registered  as  to 
principal  only  (the  first  custom  prevails  generally),  and  may  be  transferred 
by  delivery  or  indorsement  accordingly.  Registered  bonds  are  always 
drawn  payable  to  some  designated  person  and  can  be  transferred  only  by 
assignment  and  registry  on  the  books  of  the  corporation. 

ORAL   EXERCISE 

1.  Examine  the  bond  on  page  266.  With  reference  to  the 
form  of  contract,  what  kind  of  a  bond  is  it  ? 

2.  How  many  interest  notes  (coupons)  would  be  attached  to 
the  full  bond? 

3.  When  was  the  bond  issued  ?  What  date  (of  maturity) 
should  be  written  on  each  interest  note  ? 

4.  What  is  the  face  of  the  bond  ?  What  rate  of  interest  does 
it  bear  ?    What  sum  should  be  written  on  each  interest  note  ? 

5.  How  may  coupon  bonds  be  transferred  ?  registered  bonds  ? 

All  bonds  are  bought  and  sold  «  and  interest " ;  that  is,  interest  should  be 
reckoned  on  the  par  value  from  the  date  of  the  last  interest  payment  to  the 
date  of  the  purchase  or  sale,  at  the  rate  which  the  bond  pays. 

6.  If  the  bond  on  page  266  was  quoted  at  105|-  when  it  was 
purchased,  how  much  did  it  cost,  mcluding  ^  %  brokerage  ? 
How  much  did  the  seller  realize  on  it,  if  sold  Aug.  1.  1915  ? 

7.  Has  the  city  or  town  in  which  you  live  any  bonded  in- 
debtedness (indebtedness  secured  by  bonds)  ?  If  so,  what  are 
these  bonds  called,  and  what  rate  of  interest  do  they  pay  ? 

8.  What  is  the  difference  in  the  meaning  of  government  bond 
and  municipal  bond  ?  Upon  what  authority  does  the  government 
issue  bonds  ?  Upon  what  authority  does  a  town  or  a  city  issue 
bonds  ?  Must  the  bond  issue  be  approved  by  the  state  in  which 
the  town  or  the  city  is  located  ? 


268  CONCISE   BUSINESS   ARITHMETIC 

The  Use  of  Bond  Tables 

297.  The  use  of  tables  for  finding  the  interest  on  notes, 
bonds,  etc.,  is  common  among  bankers  and  brokers.  No  interest 
tables  are  illustrated  in  this  connection  because  they  are  too 
extended  and  complex  for  a  textbook. 

Referring  to  the  bond  table,  page  269,  the  per  cents  at  the  top  of 
the  table  represent  the  income  on  the  face  of  a  bond  at  one  of 
the  given  rates,  and  the  per  cents  given  in  the  column  at  the  left 
represent  the  income  that  will  be  realized  when  a  bond  is  bought 
at  a  certain  market  price.  This  table  is  for  a  bond  maturing  20 
yr.  from  date,  with  interest  payable  semiannually. 

298.  Example.  What  will  be  the  net  income  on  a  5  %  bond 
bought  at  97.53? 

Solution.  In  the  column  headed  5%  find  the  price  named,  97.53,  then  fol- 
low this  line  to  the  left  and  note  that  in  the  Ter  Cent  per  Annum  column  5.20 
is  given;  the  net  income  on  the  price  paid  for  the  bond,  97.53,  will  be  6.2%. 

ORAL   EXERCISE 

Mefer  to  the  table  and  find  the  cost  of: 

1.  A  6  %  bond  that  will  net  6J  %. 

2.  A  3  %  bond  that  will  net  5  %. 

3.  A  41  %  bond  that  will  net  4.8  %. 

4.  A  4  %  bond  that  will  net  6^  %. 

5.  A  man  purchased  4  bonds,  as  follows :  a  3  %  bond  that 
would  net  4.6  % ;  a  4^^  %  bond  that  would  net  4  % ;  a  5  %  bond 
that  would  net  4i^  %.     What  did  he  pay  for  each  bond  ? 

Refer  to  the  table  and  find  the  net  income  of: 

6.  A  5%  bond  that  willcost  $91.15. 

7.  A  7%  bond  that  will  cost  $125.10. 

8.  A  3%  bond  that  will  cost  $79.95. 

9.  A  6  %  bond  that  will  cost  $106.02. 

10.  A  man  purchased  5  bonds  each  of  which  netted  him  5  % 
income.  If  the  bonds  which  he  bought  yielded,  on  the  face 
value,  the  following  rate  of  income,  what  did  he  pay  for  each 
one:  4%,  3^%,  5%,  6  %,  and  7%  ? 


STOCKS  AND   BONDS 


269 


A  BOND   TABLE 
20-YEAR.    Interest  Payable  semiannually 


Per  CE>rT 
PER  Annum 

3% 

H% 

4% 

^7o 

5% 

6% 

7% 

3.70 

90.17 

97.19 

104.21 

111.24 

118.26 

132.30 

146.35 

31 

89.51 

96.50 

103.50 

110.49  ■ 

117.48 

131.46 

145.44 

3.80 

88.86 

95.82 

102.78 

109.74 

116.70 

130.63 

144.55 

3^ 

87.90 

94.81 

101.73 

108.64 

115.56 

129.39 

143.22 

3.90 

87.58 

94.48 

101.38 

108.28 

115.18 

128.98 

142.78 

4. 

86.32 

93.16 

100.00 

106.84 

113.68 

127.36 

141.03 

4.10 

85.09 

91.86 

98.64 

105.42 

112.20 

125.76 

139.32 

•4i 

84.78 

91.54 

98.31 

105.07 

111.84 

125.37 

138.90 

4.20 

83.87 

90.59 

97.31 

104.03 

110.75 

124.19 

137.63 

4i 

83.27 

89.96 

96.65 

103.35 

110.04 

123.42 

136.80 

4.30 

82.68 

89.34 

96.00 

102.60 

109.33 

122.65 

135.98 

4| 

81.80 

88.42 

95.04 

101.65 

108.27 

121.51 

134.75 

4.40 

81.51 

88.11 

94.72 

101.32 

107.93 

121.14 

134.35 

4i 

80.35 

86.90 

93.45 

100.00 

106.55 

119.65 

132.74 

4.60 

79.22 

85.72 

92.21 

98.70 

105.19 

118.18 

131.16 

# 

78.94 

85.42 

91.90 

98.38 

104.86 

117.82 

130.77 

4.70 

78.11 

84.55 

90.99 

97.43 

103.86 

116.74 

129.61 

4i 

77.57 

83.98 

90.39 

96.80 

103.20 

116.02 

128.84 

4.80 

77.02 

83.40 

89.79 

96.17 

102.55 

115.32 

128.08 

4i 

76.22 

82.56 

88.90 

95.24 

101.59 

114.27 

126.95 

4.90 

75.95 

82.28 

88.61 

94.94 

101.27 

113.92 

126.58 

5. 

74.90 

81.17 

87.45 

93.72 

100.00 

112.55 

125.10 

5.10 

73.86 

80.09 

86.31 

92.53 

98.76 

111.20 

123.65 

5i 

73.61 

79.82 

86.03 

92.24 

98.45 

110.87 

123.29 

5.20 

72.85 

79.02 

85.19 

91.36 

97.53 

109.87 

122.22 

5i 

72.34 

78.49 

84.64 

90.78 

96.93 

109.22 

121.51 

5.30 

71.85 

77.97 

84.09 

90.21 

96.33 

108.57 

120.81 

5f 

71.11 

77.19 

83.27 

89.36 

95.44 

107.60 

119.77 

6.40 

70.87 

76.94 

83.01 

89.07 

95.14 

107.28 

119.42 

51 

69.90 

75.92 

81.94 

87.96 

93.98 

106.02 

118.06 

^ 

68.72 

74.68 

80.64 

86.59 

92.55 

104.47 

116.38 

51 

67.57 

73.46 

79.36 

85.26 

91.15 

102.95 

114.74 

5i 

66.43 

72.27 

78.11 

83.95 

89.78 

101.46 

113.13 

6. 

65.33 

71.11 

76.89 

82.66 

88.44 

100.00  * 

111.56 

6i 

64.25 

69.97 

75.69 

81.41 

87.13 

98.57 

110.01 

6i 

63.19 

68.85 

74.51 

80.18 

85.84 

97.17 

108.50 

6f 

62.15 

67.76 

73.36 

78.07 

84.58 

95.79 

107.01 

6i 

61.14 

66.69 

72.24 

77.79 

83.34 

94.45 

105.55 

6f 

60.14 

65.64 

71.14 

76.64 

82.13 

93.13 

104.12 

6t 

59.17 

64.62 

70.06 

75.50 

80.95 

91.83 

102.72 

^ 

58.22 

63.61 

69.00 

74.39 

79.78 

90.57 

101.35 

7. 

57.29 

62.63 

67.97 

73.31 

78.64 

89.32 

100.00 

270 


COKCISE   BUSINESS   AEITHMETIC 


Buying  and  Selling  Bonds 

299.  Bonds  are  generally  bought  and  sold  through  invest- 
ment bankers  or  private  bankers. 

The  commission  for  buying  and  selling  bonds  is  the  same  as 
for  buying  and  selling  stocks. 

300.  The  following  table  is  an  abbreviated  form  of  the  sales, 
and  the  opening,  highest,  lowest,  and  closing  prices  of  bonds 
traded  in  on  the  New  York  Exchange  on  a  recent  date. 

Table  of  Sales  and  Range  of  Prices 


Sales 

Bonds 

Open. 

High. 

Low. 

Clos. 

Net  Change 

5,000 

Am.  Hide  &  Leather 

6s 

103^- 

103^ 

103 

104 

+  f 

8,000 

Brooklyn  Rapid  Tran- 

sit con, 6s .     .     .     . 

103 

103 

102f- 

103 

6,000 

Cliesapeake  &  Ohio  5s 

106i 

107i 

1061 

107i 

+  1 

81,000 

Chicago,  Burlington  & 

Quincy  4s      .     .     . 

931 

931- 

92| 

92| 

-1 

15,000 

Erie  1st  con.  4s     .     . 

85| 

8of 

85 

85 

-f 

1,000 

Illinois  Central  4s  .     . 

93  .V 

93i 

93i 

93i 

11,000 

Lehigh  Valley  con.  4^8 

99f 

99i 

m 

99i 

-f 

1,000 

Louisville  &  Nashville 

gold  5s      .... 

103 

110 

110 

110 

+  2 

2,000 

Manhattan  Ry.con,43 

92 

92i 

91f 

91i 

-i 

8,000 

Missouri  Pacific  4s     . 

59 

57 

56 

56 

-2 

24,000 

N.Y.  Central  &  Hud- 

son River  4s  1934  . 

m 

91| 

89i 

90 

-n 

35,000 

Reading  general  4s    . 

94f 

95 

94i 

941 

-i 

1,000 

Standard  Gas  6s    .     . 

89f 

89f- 

89i- 

89 

-1- 

4,000 

Texas  Pacific  1st  5s  . 

102 

102^ 

101| 

1021 

+  i 

62,000 

Union  Pacific  1st  4s  . 

97i 

971 

97i 

96f 

-f 

196,000 

United  Steel  5s      .     . 

102i 

1021- 

102i 

1011 

-f 

18,000 

Wabash  1st  5s  .     .     . 

1031 

104 

103i 

1021 

-1 

8,000 

West  Shore  4s  .     .     . 

93f 

94 

-93f 

93.V 

-i 

In  the  first  column  is  shown  the  par  value  of  the  bonds  sold ;  in  the 
second,  the  name  of  the  bonds  and  the  interest  they  bear;  in  the  third, 
fourth,  fifth,  and  sixth,  respectively,  the  oj^ening,  highest,  lovrest,  and 
closing  prices  of  the  day.  In  the  last  column.  Net  Change,  the  net  changes 
between  the  closing  prices  of  the  given  day  and  the  closing  prices  of  the 
day  preceding.  Thus,  on  the  day  given,  $8000  worth  of  Brooklyn  Rapid 
Transit  bonds  bearing  5  %  interest  were  sold.  The  opening  price  was  $  103 
per  $  100  of  par  value ;  the  highest  price,  $  103  ;  the  lowest  price,  $  102.62J ; 
the  closing  price,  $  103  ;  there  was  no  change  between  the  closing  price  of 
the  day  given  and  the  day  preceding. 


STOCKS   AND   BONDS  271 

301.  Example.  What  is  the  cost  of  S  50,000  (par  value) 
Chicago,  BurUngton  &  Quincy  4  %  bonds  at  the  highest  price 
quoted  in  the  table  (page  270)  ? 

Solution.   $100  of  par  value  cost  $93|  +  $0.12^  brokerage,  or  $94. 

.-.  $50,000  of  par  value  w^ill  cost  500,  i.e.,  ($50,000-7- $100)  times  $94,  or$47,000. 

WRITTEN  EXERCISE 

(Omit  the  interest  in  solving  these  problems) 

1.  What  is  the  cost  of  $25,000  American  Hide  and  Leather 
bonds  at  the  opening  price  in  the  table  ? 

2.  I  gave  my  broker  orders  to  sell  S  10,000  Chesapeake  & 
Ohio  5  %  bonds  and  buy  $10,000  Texas  Pacific  1st  5  %  bonds. 
If  he  sold  at  the  highest  price  in  the  table  and  bought  at  the 
lowest  price,  what  balance  should  he  place  to  my  credit  ? 

3.  Find  the  proceeds  from  these  sales :  $1000  United  Steel  5  % 
bonds  at  the  opening  price  in  the  table;  $5000  Illinois  Central 
4  %  bonds  at  the  opening  price  in  the  table ;  $  75,000  Chicago, 
Burlington  &  Quincy  4  ^o  bonds  at  the  closing  price  in  the  table ; 
$10,000  Erie  4%  bonds  at  the  lowest  price  in  the  table. 

4.  June  1, 1915,  a  certain  city  borrowed  $  250,000  with  which 
to  build  a  new  high  school,  and  issued  41  %  10-yr.  coupon  bonds 
as  security.  If  these  bonds  sold  (through  a  broker)  at  101 1-, 
how  much  was  received  by  the  city?  If  A  bought  five  $1000 
bonds,  how  much  did  they  cost  him?  If  interest  is  payable 
semiannually,  what  date  (of  maturity)  should  the  last  interest 
note  of  each  bond  bear?  What  will  be  the  amount  of  each 
interest  note  ? 

5.  Find  the  total  cost  of  the  following  purchases:  $20,000 
Erie  4  %  bonds  at  the  closing  price  in  the  table ;  $  2000  Illinois 
Central  4  %  bonds  at  the  lowest  price  in  the  table ;  $  5000  Louis- 
ville &  Nashville  5  %  bonds  at  the  lowest  price  in  the  table ; 
$15,000  Missouri  Pacific  4  %  bonds  at  the  opening  price  in  the 
table;  $10,000  Manhattan  Railway  4  %  bonds  at  the  lowest  price 
in  the  table ;  $3000  West  Shore  4  %  bonds  at  the  opening  price 
in  the  table. 


APPENDIX   A 


ADDING   MACHINES 


Machines  or  mechanical  devices  for  performing  arithmetical  calculations  are 
now  commonly  used  in  business  offices ;  in  banks,  factories,  insurance  offices, 
and  wholesale  and  retail  houses  they  may  be 
regarded  as  indispensable. 

A  machine  will  list  and  add  figures  in  one 
fifth  or  one  sixth  of  the  time  in  which  the 
work  can  be  done  by  a  person  using  a 
pen  or  a  pencil,  and  with  an  accuracy 
that  a  person  cannot  equal.    The 
operations  of  subtraction,  multi- 
plication,   division,    and    trade 
discount  may  be  as  readily  per- 
formed as  those  in  addition. 

The   machine  writes  figures 
as  rapidly  as  a  typewriter,  and 
as  legibly ;  figures  are  recorded 
by  simply  touching  the   keys. 
The   figures  written  down   are 
added  automatically,  and  at  any 
time,  by  the  mere  operation  of  a 
handle,  will  be  recorded  without 
the  possibility  of  an  error,  the 
absolutely  correct  total.     When 
an  item  is  incorrectly  put 
into  the  keyboard,  it  may, 
before  pulling  the  handle,  be 
corrected. 

Machines  are  of 
different  sizes,  and 
some  machines  have 
paper  carriages  simi- 
lar to  the  carriage 
on  a  typewriter ;  on 
these    carriages,    if 
desired,  results  are 
printed  and  carbon 
copies  made.     Ma- 
chines   may    be 
furnished     wit'.i 
an  electric  drive, 
thus  avoiding  the 
handle  pull. 

273 


274 


CONCISE   BUSINESS   ARITHMETIC 


Machines  can  be  equipped  for  adding  dollars  and  cents;  feet  and  inches; 
dozens  and  gross ;  hours  and  minutes ;  tons  and  hundred  weights ;  pounds  and 
bushels;  grains  and  penny- 
weights; English  pounds,  shil- 
lings, and  pence,  or  any  other 
kind  of  foreign  money ;  dates  and 
amounts ;  or  any  kind  of  figures. 
Machines  may  be  equipped 
with  the  unlimited  split  device 
for  dividing  the  keyboard  into 
two  or  more  sections,  for  listing 
and  adding  two  or  more  sets  of 
figures  at  one  operation.  Thus 
they  may  also  be  equipped  with 
devices  for  automatically  listing 
and  adding  across  the  sheet  or 
form  in  two  or  more  columns. 
There  is  a  duplex  adding  machine 
with  two  sets  of  wheels,  to  accumulate  two 
separate  totals  at  the  same  time.  With  a  ma- 
chine of  this  type,  totals  of  groups  of  items 
may  be  secured  and  a  grand  total  of  the 
group  totals  accumulated  at  the  same  time. 
Adding-subtracting  machines  add  debits, 
subtract  credits,  and  automatically  compute 
the  difference  and  print  it.  There  are  special 
adding  machines  for  handling  monthly 
statements  and  for  ledger  posting  and  cost 
accounting ;  a  pay-roll  machine  that,  with  one  operation,  prints  the  employees' 
numbers  and  the  amount  of  pay  on  the  pay-roll  sheet  and  pay  envelopes. 

The  following  are  some  of  the  uses  of  these 
machines  in  offices :  proving  daily  postings ;  daily 
ledger  balance ;  daily  cash  balance ;  daily  reca- 
pitulation of  sales  (as  cash,  credit,  C.O.D.,  etc.) ; 
checking   invoices    and   freight   bills;    figuring 
discounts;    computing  commissions;    summary 
of  day's  receipts  and  disbursements;   figuring 
estimates;   making  out  pay  envelopes; 
analysis  of  outstanding  accounts ;  analy- 
sis of  accounts  payable ;  balancing  petty 
cash  account;  footing  ledger  accounts 
before  taking  the  trial  balance ;  taking 
off  the  trial-balance  figures  (debits  and 
credits);  reconciling  cashbook  balance 
with  bank  balance,  listing  the  number 
and  the  amount  of   each   outstanding 
check ;  making  monthly  statements  giv- 
ing month,  date,  total  of  debits,  total  of 
credits,  balance  and  special  terms ;  compiling  statements  of  cost  of  production ; 
footing  inventories  and  calculating  extensions ;  posting  customers'  ledger. 
The  cuts  show  various  types  of  calculating  machines. 


APPENDIX   B 

TABLES    OF   MEASURES 

MEASURES  OF  CAPACITY 

Liquid  Measure  Dry  Measure 

4  gills     =  1  pint  2  pints    =  1  quart 

2  pints    =  1  quart  8  quarts  =  1  peck 

4  quarts  =  1  gallon  4  pecks  =  1  bushel 

=  231  cubic  inches  =  2150.42  cubic  inches 

Barrels  and  hogsheads  vary  in  size  ;  but  in  estimating  the  capacity  of  tanks 
and  cisterns  31.5  gal.  are  considered  a  barrel,  and  2  bbl.,  or  63  gal.,  a  hogshead. 

A  heaped  bushel,  used  for  measuring  apples,  corn  in  the  ear,  etc.,  equals 
2747.71'  cu.  in.  A  dry  quart  equals  67.2  cu.  in.,  and  a  liquid  quart  57.75 
cu.  in. 

MEASURES  OF  WEIGHT 
Avoirdupois  Weight  Troy  Weight 

16  ounces  =  1  pound  24  grains  =  1  pennyweight 

100  pounds  =  1  hundredweight  20  pennyweights  =  1  ounce 

2000  pounds  =  1  ton  12  ounces  =  1  pound 

Apothecaries^  Weight  Comparative  Weights 

20  grains     =  1  scruple  1  lb.  troy  or  apothecaries'  =  5760  gr. 

3  scruples  =  1  dram  1  oz.  troy  or  apothecaries'  =    480  gr. 

8  drams     =  1  ounce  1  lb.  avoirdupois                 =  7000  gr. 

12  ounces    =  1  pound  1  oz.  avoirdupois                 =  437^  gr. 

The  ton  of  2000  lb.  is  sometimes  called  a  short  ton.  There  is  a  ton  of  2240  lb. , 
called  a  long  ton,  used  in  all  customhouse  business  and  in  some  wholesale  trans- 
actions in  mining  products. 

In  weighing  diamonds,  pearls,  and  other  jewels,  the  unit  generally  employed 
is  the  carat,  equal  to  3.2  troy  grains.  The  term  " carat"  is  also  used  to  express 
the  number  of  parts  in  24  that  are  pure  gold.  Thus,  gold  that  is  14  carats  fine 
is  II  pure  gold  and  \%  alloy. 

Miscellaneous  Weights 

1  keg  of  nails       =  100  pounds  1  barrel  of  salt  =  280  pounds 

1  cental  of  grain  =  100  pounds  1  barrel  of  flour  =  196  pounds 

1  quintal  of  fish  =  100  pounds  1  barrel  of  pork  or  beef  =  200  pounds 

A  cubic  foot  of  water  contains  about  7|  gal.  and  weighs  62^  lb.,  avoirdupois. 

276 


276 


CONCISE   BUSIKESS   ARITHMETIC 


MEASURES  OF  EXTENSION 


Long  Measure 


12  inches  =  1  foot 

3  feet  =  1  yard 

5^  yards,  or  16|  feet  =  1  rod 
320  rods,  or  5280  feet  =  1  mile 

City  lots  are  usually  measured  by  feet  and  decimal  fractions  of  a  foot ;  farms, 
by  rods  or  chains. 


Surveyors*  Long  Measure 

7.92  inches  =  1  link 

25  links  =  1  rod 

4  rods,  or  100  links  =  1  chain 
80  chains  =  1  mile 


Miscellaneous  Long  Measures 

4  inches  =  1  hand 

6  feet  =  1  fathom 

120  fathoms  =  1  cable  length 

1.15  miles,  nearly,  =  1  knot,  or 
1  nautical  or  geographical  mile 


Square  Measure 

144  square  inches  =  1  square  foot 
9  square  feet      =  1  square  yard 
30^  square  yards  =  1  square  rod 
160  square  rods     =  1  acre 
640  acres  =  1  square  mile 


The  hand  is  used  in  measuring  the  height  of  horses  at  the  shoulder.  The 
fathom  and  cable  length  are  used  by  sailors  for  measuring  depths  at  sea.  The 
knot  is  used  by  sailors  in  measuring  distances  at  sea.  Three  knots  are  frequently 
called  a  league. 


Surveyors^  Square  Measure 

625  square  links    =  1  square  rod 
16  square  rods     =  1  square  chain 
10  square  chains  =  1  acre 

640  acres  =  1  square  mile 

36  square  miles   =  1  township 


Cubic  Measure 

1728  cubic  inches  =  1  cubic  foot 
27  cubic  feet     =  1  cubic  yard 
128  cubic  feet     =  1  cord 

1  cubic  yard    =  1  load  (of  earth,  etc.) 
24|  cubic  feet     =  1  perch 


The  square  rod  is  sometimes  called  a  perch.  The  word  rood  is  sometimes 
used  to  mean  40  sq.  rd.  or  \  A.  In  the  government  surveys,  1  sq.  mi.  is  called 
a  section. 

The  perch  of  stone  or  masonry  varies  in  different  parts  of  the  country  ;  but 
it  is  usually  considered  as  1  rd.  long,  1  ft.  high,  and  li  ft.  thick,  or  24|  cu.  ft. 


Angular  Measure 


60  seconds  =  1  minute 
60  minutes  =  1  degree 


90  degrees  =  1  right  angle 
360  degrees  =  1  circumference 


Angular  (also  called  circular)  measure  is  used  principally  in  surveying,  navi- 
gation, and  geography  for  measuring  arcs  of  angles,  for  reckoning  latitude  and 
longitude,  for  determining  locations  of  places  and  vessels,  and  for  computing 
difference  of  time. 

A  minute  of  the  earth's  circumference  is  equal  to  a  geographical  mile.  A 
degree  of  the  earth's  circumference  at  the  equator  is  therefore  equal  to  about 
69  statute  miles. 


TABLES  OF  MEASURES  277 

MEASURES  OF  TIME 

60  seconds  =  1  inimite  12  months  =  1  year 

60  minutes  =  1  hour  360  days       =  1  commercial  year 

24  hours      =  1  day  ,  365  days       =  1  common  year 

7    days        =  1  week  366  days       =  1  leap  year 

30  days        =  1  commercial  month  100  years      =  1  century 

September,  April,  June,  and  November  have  30  da.  each ;  all  of  the  other 
months  have  31  da.  each,  except  February,  which  has  28  da.  in  a  common  year 
and  29  da.  in  a  leap  year. 

Centennial  years  that  are  divisible  by  400  and  other  years  that  are  divisible 
by  4  are  leap  years. 

In  running  trains  across  such  a  broad  stretch  of  country  as  the  United  States, 
it  is  highly  important  to  have  a  uniform  time  over  considerable  territory.  Rec- 
ognizing this,  in  1883,  the  raih'oad  companies  of  tlie  United  States  and  Canada 
adopted  for  their  own  convenience  a  system  of  standard  time.  This  system 
divides  the  United  States  into  four  time  belts,  each  covering  approximately  15° 
of  longitude,  7^°  of  which  are  east  and  7^°  west  of  the  governing  meridian.  The 
region  of  eastern  time  lies  approximately  7|°  each  side,  of  the  75th  meridian, 
and  the  time  throughout  this  belt  is  the  same  as  the  local  time  of  the  75th  merid- 
ian. Similarly,  the  regions  of  central,  mountain,  and  Pacific  time  lie  approxi- 
mately 7^°  each  side  of  the  90th,  105th,  and  120th  meridians,  respectively,  and 
the  time  throughout  each  belt  is  determined  by  the  local  time  of  the  governing 
meridian  of  that  belt.  There  is  just  one  hour's  difference  between  adjacent  time 
belts.  Thus,  when  it  is  11  o'clock  a.m.  by  eastern  time,  it  is  10  o'clock  a.m.  by 
central  time,  9  o'clock  a.m.  by  mountain  time,  and  8  o'clock  a.m.  by  Pacific  time. 
Since  railroad  companies  change  the  time  at  important  stations  and  termini, 
regardless  of  the  longitude  of  such  stations  and  termini,  the  boundaries  of  the 
time  belts  are  quite  irregular. 

MEASURES  OF  VALUE 
United  States  Money  English  Money 

10  mills     =1  cent  4  farthings  =  1  penny 

10  cents     =  1  dime  12  pence       =  1  shilling 

10  dimes   =  1  dollar  20  shillings  =  1  pound  sterling 

10  dollars  =  1  eagle  =  $4.8665 

The  term  "  eagle  "  is  seldom  used  in  business.  The  mill  is  not  a  coin,  but  the 
name  is  frequently  used  in  some  calculations.  In  Canada  the  units  of  money 
are  the  same  as  in  the  United  States.     1  far.  =  |§^  ;  Id.  =  2,^^^^  ;  Is.  =  24^ f. 

French  Money  German  Money 

100  centimes  =  1  franc  =  1 0.193  100  pfennigs  =  1  mark  =  $0,238 

MISCELLANEOUS  MEASURES 

Counting  by  12  Counting  Sheets  of  Paper 

12  things  =  1  dozen  24  sheets  =  1  quire 

12  dozen   =  1  gross  20  quires  =  1  ream 
12  gross    =  1  great  gross  =  480  sheets 


278 


CONCISE   BUSINESS   ARITHMETIC 


BUSINESS   ABBREVIATIONS 


A  .    . 

.  acre 

Mar.  .     . 

.  March 

Apr.  . 

.  April 

I^Idse.      . 

.  merchandise 

Aug.  . 

.  August 

Messrs.    . 

.  Messieurs,    Gentlemen  ; 

bbl.    . 

.  barrel;  barrels 

Sirs 

bdl.    . 

.  bundle;  bundles 

mi.     .     . 

.  mile;  miles 

bg.      . 

.  bag;  bags 

.  basket;  baskets 

min.   .     . 

.  minute;  minutes 

bkt.    . 

mo.     .     . 

.  month ;  mouths 

bl.      . 

.  bale;  bales 

Mr.     .     . 

.  Mister 

bu.      . 

.  bushel;  bushels 

Mrs.   .     . 

.  Mistress 

bx.      . 

.  box;  boxes 

N.       .    . 

.  north 

cd.      . 

.  cord;  cords 

No.     .     . 

.  number 

ch.      . 

.  chain ;  chains 

Nov.  .     . 

.  November 

c.i.f.    . 

.  carriage  and  insurance  free 

Oct.    .     . 

.  October 

Co.     . 

.  company;  county 

oz.       .      . 

.  ounce;  ounces 

C.O.D. 

.  collect  on  delivery 

p.  .  .   . 

.  page 

Coll.  . 

.  collection 

pc.       .     . 

.  piece;  pieces 

Cr.      . 

.  creditor;  credit 

per.     .     . 

.  by  the ;  by 

CS. 

.  case;  cases 

per  cent. 

.  per  centum,  by  the  hun- 

ct.      . 

.  cent;  cents;  centime 

dred 

cu.  ft. 

.  cubic  foot ;  cubic  feet 

pk.      .     . 

.  peck;  pecks 

cu.  in. 

.  cubic  inch ;  cubic  inches 

pkg.   .    . 

.  package;  packages 

cu.  yd. 

.  cubic  yard ;  cubic  yards 

pp.     .    . 

.  pages 

cwt.    . 

.  hundredweight 

pr.      .    . 

.  pair;  pairs 

d.  .     . 

.  pence 

pt.      . 

.  pint;  pints 

da.      . 

.  day;  days 

pwt.    .     . 

.  pennyweight;      penny- 

Dec.   . 

.  December 

weights 

doz.    . 

.  dozen;  dozens 

qr.      .     . 

.  quire;  quires 

Dr.      . 

.  debtor;  debit;  doctor 

qt.      .     . 

.  quart;  quarts 

E.  .     . 

.  east 

rd.       . 

.  rod ;  rods 

ea. 

.  each 

rm.     . 

.  ream  ;  reams 

e.g.     . 

.  exempli    gratia,      for    ex- 

Rm.(or B 

I.)  Reichsmark,  Mark 

ample 

s.    .     . 

.  shilling;  shillings 

etc.     . 

.  et  ccetera,  and  so  forth 

S.  .    . 

.  South 

far.     . 

.  farthing;  farthings 

sec.     . 

.  second;  seconds 

Feb.   . 

.  February 

sq.  ch. 

.  square     chain;    square 

f.o.b.  . 

.  free  on  board 

chains 

fr.       . 

.  franc;  francs 

sq.  ft.      . 

.  square  foot;  square  feet 

ft.       . 

.  foot;  feet 

sq.  mi. 

.  square      mile;      square 

gal.     . 

.  gallon;  gallons 

miles 

gi-       • 

.  gill;  gills 

sq.  rd. 

.     .  square  rod;  square  rods 

gr.       . 

.  grain ;  grains 

sq.  yd. 

.     .  square     yard;     square 

gi-o.     . 

.  gross 

.  hogshead;  hogsheads 

yards 

hlid.    . 

T.  .    , 

.     .  ton 

hf.  cht. 

.  half  chest ;  half  chests 

tb.      . 

.     .  tub;  tubs 

hr.      . 

.  hour;  hours 

Tp.     . 

.     .  township;  townships 

i.e. 

.  id  est,  that  is 

viz.     . 

.     .  videlicet,  namely ;  to  wit 

in. 

.  inch;  inches 

via     . 

.     .  by  way  of 

Jan.    . 

.  January 

wk.     . 

.    .  week;  weeks 

kg.     . 

.  keg;  kegs 

wt.     . 

.     .  weight;  weigh 

1.    .    . 

.  link ;  links 

yd.     . 

.     .  yard;  yards 

lb.      . 

.  pound;  pounds 

yr.      . 

.     .  year;  years. 

BUSINESS   SYMBOLS  AND  ABBREVIATIONS      279 


«/<j  account 

«/s  account  sales 

+  addition 
(  )  ~  aggregation 

&  and 

and  so  on 

@  at;  to 

c/o  care  of 

^  cent;  cents 

y/  check  mark 

°  degree 

-h  division 

$  dollar;  dollars 


BUSINESS   SYMBOLS 

=    equal;  equals 
'       foot;  feet; 

minutes 
C     hundred 

"      inch ;  inches ;  seconds 
X     multiplication 
;J^    number,  if  written 

before  a  figure; 
pounds,  if  written 

after  a  figure 
1^     one  and  one  fourth 
V    one  and  two  fourths ; 

one  and  one  half 


1^    one  and  three 

fourths 
^     per;  by 
%     per  cent ; 

hundredth ; 
hundredths 
£      pounds  sterling 

since 
—     subtraction 

therefore 
M    thousand 
Ye    5  shillings  6  pence  ; 
five  sixths 


INDEX 


Abbreviations,  278 
Above  par,  258 
Abstract  number,  36 
Adding  machines,  273 
Addition,  2,  78,  107,  172 
Aliquot  parts,  138 
Amount,  176,  232 
Angular  measure,  276 
Apothecaries'  weight,  275 
Assessment,  257,  260 
At  a  discount,  254,  258 
At  par,  254 

At  a  premium,  254,  258 
Average  clause,  211 
Avoirdupois  weight,  275 

Bank  discount,  230,  231 

Bank  drafts,  246,  248 

Bank  loans,  238 

Bank  money  order,  243 

Banker's  sixty-day  method  of  interest, 

219 
Banking,  216 
Base,  176,  180 
Below  par,  258 
Bill  of  lading,  254 
Bills,  31,  32,  45,  49,  116,  145,  146,  150, 

151, 152,  153, 154,  155, 156,  161, 165, 

190,  208 
Bills  and  accounts,  150 
Blanket  policy,  210 
Bond  table,  269 
Bonds,  265,  266 
Buying  bonds,  270 
Buying  by  the  hundred,  89 
Buying  by  the  thousand,  89 
Buying  by  the  ton,  90 
Buying  stocks,  262 

Cable  length,  276 
Cancellation,  97 
Capital  stock,  256 
Carat,  275 
Cashier's  check,  249 
Certificate  of  deposit,  249 
Change  memorandum,  159 
Charter,  256 


Checking  results,  12,  24,  38,  43,  44,  55, 

71   72   73 
Checks,  246, 250,  260 
Clearing  house,  246,  247 
Code,  244 
Co-insurance,  211 
Collateral  note,  240 
Collateral  trust  bond,  265 
Collection  and  exchange,  236,  252 
Commercial  bank,  230 
Commercial  discounts,  188 
Commercial  drafts,  231,  252 
Common  denominator,  106 
Common  divisor,  98 
Common  fractions,  101 
Common  stock,  258 
Comparative  weights,  275 
Complement,  27 
Composite  number,  95 
Concrete  number,  36 
Consecutive  numbers,  10 
Conversion  of  fractions,  127 
Corporation,  256 
Counting  by  12,  277 
Counting  sheets  of  paper,  277 
Coupon  bond,  266 
Cubic  measure,  276 

Day  method  of  interest,  217 

Days  of  grace,  231 

Debenture  bonds,  265 

Decimal,  75 

Decimal  fractions,  75 

Decimal  units,  75 

Demand  note,  239 

Denominate  quantities,  169 

Denominator,  101 

Deposit  slip,  251 

Depositors'  ledger,  30,  34,  35,  50 

Difference,  176 

Discount  series,  188,  191 

Dividend,  52,  257,  260 

Division,  52,  57,  85,  88,  121,  173 

Divisor,  52 

Divisors,  98 

Domestic  exchange,  242 

Drafts,  230,  231,  238,  252 


281 


282 


CONCISE  BUSINESS  ARITHMETIC 


Drawee,  231 
Drawer,  231 
Dry  measure,  275 

English  money,  277 
Even  number,  95 
Exchange,  242,  249 
Exponent,  36 
Express  money  order,  243 
Expressage,  164 

Factor,  36,  95 

Factoring,  96 

Fathom,  276 

Final  results,  105 

Finding  the  base,  180 

Finding  the  cost,  199 

Finding  the  gain  or  loss,  197 

Finding  the  per  cent  of  gain  or  loss, 

198 
Finding  the  percentage,  176 
Finding  the  rate,  178 
Fire  insurance,  209 
Fire  losses,  133,  134 
Firm  note,  236 
Fixed  policy,  210 
Floating  policy,  210 
Fluctuation  of  rates  of  exchange,  254 
Fractional  relations,  124 
Fractions,  75 
Freight  bill,  165 
Freightage,  164 
French  money,  277 

Gain  and  loss,  196 

Gain  or  loss  on  selling  price,  202 

German  money,  277 

Government  bonds,  265 

Graphic  representations,  126, 133, 185 

Greatest  common  divisor,  98 

Gross  price,  189 

Gross  weight,  30 

Grouping,  3,  6 

Hand,  276 
Heaped  bushel,  275 
Holder,  230 
Horizontal  addition,  16 

Important  per  cents,  176 
Improper  fraction,  102 
Income  bond,  265 
Insurance,  209 
Insurance  rates,  213 
Insurer,  210 


Interest,  216 
Invoice,  150 

Joint  and  several  note,  236 
Joint  note,  236 

Key,  204 
Knot,  276 

League,  276 

Least  common  denominator,  106 

Least  common  multiple,  100 

Letter  ordering  goods,  162 

Liquid  measure,  275 

Listing  goods  for  catalogues,  207 

Long  measure,  276 

Long  ton,  275 

Making  change,  25 

Market  value,  258 

Marking  goods,  204 

Maturity,  230 

Maturity  table,  232 

Measures  of  capacity,  275 

Measures  of  extension,  276 

Measures  of  time,  277 

Measures  of  value,  277 

Measures  of  weight,  275 

Miscellaneous  measures,  277 

Miscellaneous  weights,  275 

Mixed  numbers,  102 

Model  figures,  11,  13,  14,  15 

Money  orders,  242 

Mortgage  bonds,  265 

Multiple,  36 

Multiplication,  36,  41,  43,  45,  46,  4T 

82,  114,  120,  173 
Municipal  bonds,  265 
Mutual  insurance  company,  210 

Net  price,  189 
Net  weight,  31 
Notation,  76 
Notes,  239,  240 
Numeration,  76 
Numeration  table,  76 
Numerator,  101 

Odd  number,  95 
Open  policy,  210 
Ordinary  policy,  210 

Par  value,  258 
Parcel  post,  63 
Parenthesis,  23 
Pay  rolls,  159,  160,  163 


IKDEX 


28a 


Payee,  231 

Pay-roll  inemorandum,  160 

Per  cent,  76,  175 

Per  cents  of  decrease,  182 

Per  cents  of  increase,  181 

Percentage,  175 

Perch,  276 

Policy,  210 

Postal  money  order,  242 

Postal  service,  63 

Power,  37 

Preferred  stock,  257 

Premium,  210 

Prime  number,  95 

Principal,  216 

Proceeds,  232 

Promissory  notes,  239,  240 

Properties  of  9,  71 

Properties  of  11,  72 

Property  insurance,  209 

Quotient,  52 

Rate,  176,  211,  216 

Rate  of  exchange,  243,  248,  254  . 

Reading  decimals,  76 

Reduction,  103,  104,  105,  106,  170, 171 

Registered  bond,  267 

Remainder,  52 

Repeaters,  204 

Review  of  the  common  tables,  169 

Review  tests,  22,  35,  51,  94,  137,  187, 

195,  241 
Rood,  276 

Scrip,  259 

Section,  276 

Selling  by  the  hundred,  89 

Selling  by  the  thousand,  89 

Selling  by  the  ton,  90 

Share,  256 

Short  methods,  41,  57,  108,  118 

Short  ton,  275 

Sight  draft,  252 

Similar  fractions,  106 

Simple  interest,  217 


Six  per  cent  method  of  interest,  227 

Sixteen  to  one,  118 

Solution  of  problems,  128 

Specific  policy,  210 

Square  measure,  276 

Standard  time,  277 

Stock  broker,  258 

Stock  certificates,  256,  257,  258 

Stock  company,  256 

Stock  insurance  company,  210 

Stockholder,  256 

Stocks  and  bonds,  256 

Subtraction,  23,  80,  112,  172 

Surveyors'  long  measure,  276 

Surveyors'  sqiiare  measure,  276 

Table  of  aliquot  parts,  140 

Table  of  bond  quotations,  270 

Table  of  common  measures,  275 

Table  of  .important  per  cents,  176 

Table  of  insurance  rates,  213 

Table  of  stock  quotations,  262 

Table  of  time,  234 

Table  of  twelfths,  206 

Tare,  30 

Tariff,  or  rate,  book,  213 

Telegram,  244 

Telegraphic  money  order,  244 

Telegraphic  rates,  245 

Term  of  discount,  232 

Terms  of  a  fraction,  102 

Tests  of  divisibility,  96 

Time  sheets,  159,  160,  163 

Time  slip,  163 

Trade  discount,  188 

Troy  weight,  275 

Underwriter,  210 
Unit  fraction,  102 
United  States  money,  277 

Value,  232 
Valued  policy,  210 
Vinculum,  23 

Weigh  tickets,  90 


CB 


YC  45042 


